I've also seen arguments that Republicans erred in opposing the treaty without having the votes to win on it; as Fred Kaplan put it:
And so the Republican leadership made this a purely political battle and—fresh off what had seemed a triumphant election season—suffered an astonishingly egregious defeat.Perhaps. On the other hand, the "defeat" aspects of this are likely to be minimal and ephemeral; a few weeks from now, no one is going to remember or care about New START (on the political side; the substance, of course, matters, but there's no difference there between fighting and losing and just plain letting the thing pass).
However, Republicans did accomplish something by fighting on New START. They chewed up quite a few hours of Senate floor time, a very valuable commodity in the lame duck session, and really throughout the 111th Congress. Now, there's really no way of knowing what exactly they gained by doing that. However, had they agreed to a quick vote on the treaty, there would have been more time for the Democrats to confirm judges and executive branch appointments; more time for appropriations bills, and perhaps to give a more sustained effort on the omnibus appropriations bill; and more time for any of the other unfinished business on the Democratic agenda.
So I wouldn't be quick to conclude that it was a mistake for Republicans to fight this one out, even if they took a (very minor) PR hit in losing. Indeed, in understanding what the GOP was up to, I think one has to consider the possibility that treaty opposition was in part a deliberate -- and, I would say, perfectly legitimate -- part of trying to run out the clock.