Water under the bridge
It's hardly fatal to his political career, but it doesn't speak well of the people who set up Rubio's address that they created a situation that made him look so awkward. We just had a rather pointed lesson on how superficial this electorate is, didn't we? One reason Obama did well is that he's always presented as polished, even regal; the media tastefully averts their gaze when he does something clumsy, but his handlers are generally pretty good at minimizing those moments. The small details must be taken care of.
Rubio's displayed a great sense of humor about "Watergate," which will defuse most of the actual damage. And don't kid yourself - it will do damage to him among the low-information voter set. The only part of his speech they're going to remember, and one of the few parts they'll even see, is the Sip of Doom. But when they see Rubio joshing about it, and if he's otherwise running a good 2016 campaign, they'll let it slide.
And there's always the chance liberals will overplay this, mocking Rubio with escalating venom until those who aren't die-hard lefties say to themselves, "Well, the guy was just delivering a big speech and he got thirsty, what's the big deal?" As you said, Debra, it will seem more endearing and human if the Flying Monkey Brigade harps on it too much.