Having read a whole bunch of this discussions, I've come to the conclusion that there are 2 types of readers.
1) Those who prefer likable characters.
2) Those who don't care as long as the main character is interesting.
I am definitely the first, and so is my father. Unlikable main characters is the reason I give for not liking The Corrections, and it's the reason my dad gives for not liking Lolita. My husband doesn't care about likability and enjoyed both those books. Of course, different readers will also find different characters likable. But the "interesting not likable" advice, which inevitably comes up, grates on me because it definitely IS a factor that affects my enjoyment of a book as a reader. There are a few books with unlikable main characters that I've enjoyed somewhat, such as Gone Girl. But it's rare, and I don't imagine I'll ever love such a book. If I am going to love a book, it better have a likable main character. And I don't seem to be alone in that.
Also, I believe there are some genres and types of stories for which likability is more important than in others. For example, I read a lot of romance. A good romance has an emotionally satisfying ending that gives you an "aww!" feeling at the end. I cannot see how that could happen if the leads are unlikable. Perhaps the worst would be if one is likable and the other is an asshole...it would feel like a tragic ending. Again, of course, different readers find different characters likable. There are many controlling, possessive alpha-holes in romance, and that baffles me.
Then there is the issue of likable vs relatable, which always comes up, too. They're not exactly the same thing, but I think how these two relate to each other also depends on the reader. Likability and relatablity may be more closely linked for some readers than others...at least, that is my impression from reading such discussions.
Anyway, I think you can have unlikable main characters, but I think you have to consider your audience and the type of story you're writing. If the MC is unlikable, there should be good reasons for it. And if you write what you think is a likable MC but readers keep telling you otherwise, you should definitely take a closer look.
I actually recently sold a book--a romance, in fact--with a cranky misanthrope as the hero, and the editor really liked him and said he was "endearingly grumpy." I think this is partly because:
1) He had relatable feelings, just a little more extreme than the average person. I mean, we've all want to be left alone at some point, right?
2) Although he didn't like people, he wasn't evil or malicious.
3) There were understandable reasons for him to be the way he was.
4) He still had a code of morals.
5) He was cranky, yes, but he wasn't annoying.
6) It was funny. (Actually, humor is the main thing that can make up for an unlikable character for me as a reader.)
It is possible to make a character likable even if they don't sound terribly likable from a brief description.