Internet people love to declare that X is "fair use", but Internet people tend to have much more confidence than they should. (For one thing, they tend to read the criteria for fair use and think it's a logical or operation, when it's more of an and. It isn't either, really, it's what a judge determines, but it's more of an "and".)
You can't really know until you're in front of a judge, but if we take a tweet as a work, publishing an entire tweet without permission seems awfully likely to fail the amount test. Taking 100% of a work doesn't seem like fair use. You're also in trouble on the "work's value" front, because it's likely that the judge will not accept that Mark Cuban's tweets are not of some value. (A judge might write my tweets off as pretty worthless, but probably not Mark Cuban's.) Being given away voluntarily by the owner does not prove they don't have value, merely that the owner perceives that they have more value to the owner in that form, value you are impinging upon by republishing out of his control.
Your best bet at this point is to try to claim that the tweet is too small to constitute a "work", and you're just excerpting the tweet stream. From this point of view you pass all the fair use tests. However, my uninformed opinion is that this is unlikely to fly, because we recognize important copyrights on small snippets of things all the time, such as advertising slogans, and in every other way, a tweet is clearly an atomic published work, being independent of all the other tweets in the stream.
Maybe with a good enough legal team and the right judge, you could win a case that republishing a tweet is fair use, but it would be an uphill battle in my opinion.
because we recognize important copyrights on small snippets of things all the time, such as advertising slogans
I believe that what we're recognizing in the case of advertising slogans is trademark, not copyright. If I'm writing on the topic of advertising, I can perfectly well say "I believe that the new slogan, 'Snickers really satisfies!' may well be the dumbest slogan I've ever heard." without any copyright concern.
At the same time, I couldn't sell a candybar with the slogan "Foonuts really satisfies" due to trademark law, not copyright law.
The fair use analysis for citing an advertising slogan is very different than it is for a tweet. You're not affecting the slogan's value the way that republishing a tweet against the author's will can, and the purpose test is more in your favor since you're probably mentioning it to be critical of it in some way.
Based on my experience, at this point I expect someone to start jumping in and trying to slice and dice their way between these standards. So let me try to preempt that a bit by reminding you that you have to be taken to court for copyright infringement before you can make a fair-use defense and that an intrinsic part of the process is the judgment of the court. The judge would laugh M&M Mars out of court if they claimed my citing "Taste the Rainbow" as a trite slogan was a copyright violation, but republishing a person's tweet is a radically different thing, and the question is not "can I weave and dance and obfuscate and blur the question on the internet?", but "can I weave and dance and obfuscate the question in front of a judge?" There is a professionally-trained human hairsplitter in the decision loop, by design.
Mind you, I might still be wrong in my analysis; I'm not saying I can't be wrong, my point is that pulling the whole dodge, weave, and obfuscate move to try to show that I'm being hypocritical or that I somehow disagree with myself is not valid.
I'm sure various aspects are trademarked too, but the story on the back of this cookie box about Knott's Berry Farm is definitely copyrighted. I trust they could sue me if I reprinted it.
Single sentence quotations are often taken as a whole because there is no other way to review them. That's why it falls under fair use, not the partial-extract part of it. Your example of advertising slogans is a perfect example actually.
Excerpting the tweet stream does seem to be a more logical view of what's going on actually.
Interesting. I'm not sure why one would assume a 'tweet' isn't copyrightable. Seems to me that the real question is the part about 'fair use'. What kind of control do you have over a tweet, even if you do have the copyright.
Publish and licence your tweets with Creative Commons: http://tweetcc.com/ The site was started after a discussion with a book publisher wanting rights to use tweets in a book.
In the context of Mark Cuban's tweet, republishing it is fair use (http://en.wikipedia.org/wiki/Fair_use).