I think the idea that the Senate GOP's obstructionism will hurt them is overblown

I believe this for two reasons:

• The government shutdown in 2013 is an example. Congress' approval rating bottomed out after at 9%, and more people (rightfully) blamed Republicans than however. So obviously, they got their asses handed to them in 2014, right? People were going to hold them accountable for refusing to govern, right? Wrong, they made huge gains in both houses. And this only helped Ted Cruz raise his profile to run for president (he won't win the nomination, but still). Not only that, their base loves this kind of political theater.

• The media. The "mainstream media" (I hate using this term, but whatever) will play the 50/50, neutrality, "both sides do it" game, meaning that even if Obama nominates a centrist, they still might perceive him as not compromising enough.

But if it did matter, all Senate Republicans would have had to do is stay quiet, and then just reject every nominee.