I really don't understand why everyone thinks this vote is the kiss of death to Republicans in Latino-heavy states. Presumably the Latinos that vote for Republicans won't be dissuaded by this vote, as they're probably conservative in the first place. Cornyn won re-election by 55-43 while losing Latinos 61-36, so it's not like he's got that much further down to go among that constituency.
It is not a huge problem in the short term, but the GOP is setting itself up poorly in the intermediate to long term. The party is already in trouble with Latino voters over immigration and other issues. If there is a solid GOP vote against Sotomayor, particularly from senators in heavy Hispanic states, perceptions of the party will continue to solidify. Crist, Kyl and Cornyn have all come out against Sotomayor, I suspect Hutchinson will as well. At the rate the Hispanic population is growing, that 61-36 margin will loom much larger in the future.
Still, Cornyn's seat is basically his as long as he wants it. For a Republican incumbent to lose a senate election in Texas would probably require a scandal of the live boy/dead girl variety. That'll probably be different in 10-15 years, but Cornyn should have retired by then.