Clint's level of commitment and fear/desire of or for it, depends on how much he is influenced by canon.
In the comics, while he was married for many years to Mockingbird, they spent more time estranged than happily married. His relationships are always kind of sabotaged by his own hand, he either picks women he has no future with or goes out of his way to screw up to avoid commitment. He is an average guy, and like most men, there is a fear of commitment hidden away inside.
The latest issue of Hawkeye has him kissing a woman in front of his girlfriend, ex-girlfriend and ex-wife and starting a brawl in a strip club as a tactic to avoid commitment. This was the Valentine's issue, and he cheats on his girlfriend with a stripper.
I think if you asked 616 comic universe Clint Barton who the greatest villain in his life was, it would be his dick, it ruins careers, relationships and lives, mostly his own because of his inability to keep it in his pants.
The Ultimate Barton, which also was a partial basis for the MCU version, had few real relationships. He had his wife and kids, his partner Black Widow and Fury, the closest thing to friend he really had. Widow killed his family, he killed Widow, so he is left with old buddy Nick Fury, who recruited him right out of jail and made him his red right hand who he can share killing and dirty jokes with, and the job. He didn't much get along with his Avengers teammates.
So we arrive at the MCU version, where with the background Marvel created to fill in the holes between the movies reveals him as something like Fury's attack/guard dog, while Romanoff is off following the Hulk and Thunderbolt Ross. This Barton is a guy who doesn't take time off from the job, and jumps when Nick gives the call to action, looking for something to shoot and annoyed when stuck with Coulson on a boring assignment in New Mexico, though Fury places him there because he trusts him and guarding the Cube is something Fury would only give to someone he really trusted.
As for Natasha, they don't seem to actually be partnered often, the two never interact outside of the movie, and so there are a few scenes that speak of an affection between them but nothing that would lead me to believe marriage or exclusive commitment was ever in the realm of discussion.
I read a lot of stories where Clint is essentially written as the normal guy and Natasha is the screwed up one, Clint has a bromance with Coulson and makes easy friends with the Avengers, which is kind of strange since Clint has always been an abrasive and confrontational personality in any universe, the guy used to pick fights with Captain America about not being a good enough leader. I think Clint is just as screwed up as Natasha, if not more, I'm not sure he would be friends with Coulson; work colleague, yes, friend, no. The Ultimate universe relationship between Fury and Barton seems more plausible than Coulson/Barton buddies, Fury trusts and likes him, and Barton seemingly feels the same way back, if that isn't an indication that this guy is messed up, I don't know what is. Clint Barton bromance with Nick Fury, just think about how frightening them sharing a beer would be.
Natasha strikes me as the type who could interact and make friends easier as well, if only superficially, due to her skill set.
Coulson seems more a Natasha buddy, very sedate and self contained people who could sit down and chat politely.
Taken together, I think Clint and Natasha far too emotionally stunted to actually survive something like marriage, sure I could see sex, (Clint Barton has never said no to a beautiful woman in any universe) but open emotion, commitment or anything that would compromise their jobs, no. These people strike me very pragmatic people who are about SHIELD first, everything else is a secondary consideration.
I mean working towards a place they could be people ready for an actual relationship, serious therapy and time. Also, Hawkeye is obviously more than a decade older than Widow (unless you are bringing the Soviet super serum thing into this universe) and I don't see him as the type of guy to actively chase a relationship with a woman much younger than him, she would have to push the issue, and I don't see Natasha as the type to push for that type of thing.

I read a lot of stories where Clint is essentially written as the normal guy and Natasha is the screwed up one, Clint has a bromance with Coulson and makes easy friends with the Avengers, which is kind of strange since Clint has always been an abrasive and confrontational personality in any universe, the guy used to pick fights with Captain America about not being a good enough leader. I think Clint is just as screwed up as Natasha, if not more

Dude this gives me life. I heart prickly, effed up Clint like whoa and I always love it when his characterization is given the same thoughtful treatment as Natasha's. And yes, in so many ways I think he's the more difficult one to deal with on a inter-personal level, the one less likely to make friends, the one far more likely to rub people the wrong way. And I kind of lvoe that about him.

Also very much digging the strange and wondrous possibility of a Clint/Fury friendship. Frightening indeed. I want that fic.

I would certainly enjoy seeing Fury written better as a whole, it seems largely that most stories essentially adopt Stark's view of Fury as something borderline evil and completely untrustworthy, while Coulson is this saintly figure. Which perplexes me somewhat, as Coulson was certainly Fury's man, anything he did was at the behest of Fury and he never showed and disloyalty to SHIELD. Coulson threatened to taser Stark and watch TV while Stark lay in a puddle of his own drool, while Fury saved Stark's life and helped him deal with his daddy issues. So I find the Stark/fan dynamic towards Coulson and Fury perplexing. Not to say either Fury is a good man or that Coulson was a bad man, just that I think they are essential more the same type of person, but get written completely inconsistent with their characters.
The Fury and Barton relationship strikes me as the more plausible, I would envision that Fury was the one to handpick Barton for SHIELD, much like how he scooped him off death row in the Ultimateverse. I think Barton's ultimate loyalty is to Nick, rather than SHIELD. Also some of the background material leads me to believe Coulson and Barton essentially share rank, rather than Coulson outranking him, and Barton essentially answers directly to Fury.
I'm sure the SHIELD dynamics may get explored in further movies because there have been rumours that much like in the comics, Maria Hill may make a push for power due to her dislike and distrust of the Avengers, and may push for the Hulk to be neutralized, and Avengers 3 will essentially be ripped straight from the comics, with it being a World War Hulk story, Stark launching Hulk into space exile to neutralize him and him coming back for revenge.

And then there is redefining the character and writing them differently/trying out different things.

I didn't read comics and really don't intend to - they're hard to get where I live, also, I tend to see MCU Clint and comic(s)!Clint as fundamentally different people - based on what you wrote here, they're very much different. Basis and some aspects might be the same, everything else is a variation of a theme.

My point is, there are lot of way to interpret something or someone. There are dark versions, light versions, silly versions. I prefer some more and some less, and I think it's great that fandom (at least this bit of it) offers room to explore all of those possibilities. I'm a type of person who will pretty much always advocate for messed up people working toward getting better (and having healthy things in their life and yes that includes relationships too; because that's what I like in my fictional things). I'm also aware that not everyone enjoys the same things I do.

It is a shame you don't read the comics or intend to, (the internet is wonderful tool to access them, either through digital copies sold by marvel or just downloading torrents).

Clint Barton is one of the great characters to come out of Marvel. This is a regular guy hanging around with superphumans. Clint honest to god really does try to be a hero, the ego on him though is insane sometimes (I mean who tells Cap to his face as a leader, you're a joke? or tells Bucky after he inherits Cap's Shield and costume that it was offered to him first and he was Bucky was second choice?) Sometimes he pulls it of spectacularly, totally backs it up and sometimes he just ends up looking like a complete ass. End of the day though, he is the only guy with no superpowers or million dollar super technology who has ever led the Avengers.

It does seem most people see Barton as fundamentally different from the comics, although that may partially be because the comics don't seem to be widely read, though I do see aspects of Barton that come through.
He has the confidence, he walks into an alien invasion with a bunch of superhumans armed only with a bow and arrows, that has the balls of the guy Clint Barton is in the comics and really at the end of the day that is the most important thing about Hawkeye, the unwavering confidence. The guy who does what he does - without powers - because he believes he is a weapon all by himself, because he believes not just that he won't miss, but can't miss. The guy who will challenge anyone to a fight, and believe he'll win.
He may not be a smart mouth on par with Spiderman, or be damn sure he is god's gift to women in the films, but he kicks super villain ass with only a stick and some string, and that takes big brass ones.

I agree with you on the cockiness -- that sure comes out in the movie when he takes on Fury at the beginning ("Well, I see better from a distance") and Thor concerning unfinished business with Loki ("Yeah? Get in line.")

But as for your comments on in-character Clint when it comes to relationships, this is the gist of something I said in another discussion: There is nothing wrong, and everything commendable, with freedom of interpretation in fan fiction. It's not called "transformative fiction" for nothing. The key is at least some consistency with the character, not slavish reproduction of his/her actions.

I don't know the comics verse well (I have read one Fraction/Aja, but what the hell is 616??) but what I have seen, based on internet research, their only consistency is inconsistency when it comes to relationship issues. Seems to me, every time a new artist gets involved there's a near-total reboot. The whole thing makes my head spin, so I tend to ignore it except for certain tombstone facts on which there appears to be consensus (dead parents, circus, a past committed relationship, that sort of thing).

Jeremy Renner himself, when he was asked whether he'd researched comic Hawkeye in preparation for his role, that he drew his interpretation of the character from what he was given in the script. Who am I to argue with that ...? ;-)

There's a million universes out there and there is no way to figure out which one is "right". I've read comics and I've been up to date on the latest Hawkeye with Matt Fraction. In that one he is played as a normal guy who just goes about living his life. He's not completely screwed up and he has a healthy friendship with Kate Bishop. It's a lighter version of Hawkeye, so as far as I am concerned having Barton be a balanced person is no more AU than anything else.

YES to all of that.

Reed Richards of the Fantastic Four in his research came across the multiverse and with the Captain Britain Corps, went about numbering the realities (because apparently that's that type of things the smartest guy in the universe does with his spare time; although it was probably just an excuse to find other Reeds and form the Council of Reeds to have someone to talk to who he didn't consider an idiot and can understand him). The core reality/primary continuity of Marvel was thus called Earth 616, everything else is considered out of continuity and takes place on a different numbered Earth, and isn't considered canon. So the Ultimateverse has a number, as does the MCU, Marvel Knights, Age of Apocalypse, etc.
As for the Clint/Kate relationship in the Hawkeye series, it's Barton's attempt at a healthy platonic relationship with a woman, as he tells her straight out he doesn't want to sleep with her so they can work together, because whenever he sleeps with someone that ensures that he will screw the relationship up.

Be that as it may, he is still relatively balanced in that universe. He isn't drowning in angst nor is he particularly angry or hateful. So portraying him as such is not AU.

Also, until Clint is dead, I, and any other fans, can choose to believe he will change. Isn't that what almost every story told is about...redemption and change. I mean there is a reason fans of Harry Potter are obsessed with writing stories for Draco. Or the reason Daryl Dixon is a fan favorite on The Walking Dead. We like to write/read stories about how humans can evolve. So in the end, I find there nothing inherently AU about many of the people's portrayal of Clint in these stories. He's never perfect, he's always rough around the edges, looking to kind of change his story and I think that is at its core what Clint is about.