They've actually been moving away from Obamacare as a political issue for a couple of years, judging by a long series of polls from the Kaiser Family Foundation. Clear back in March 2011 only the most rabid supported repeal of the law. That continued in November 2011. In July, 2012 a few months before a national election proved it, a healthy majority of 56 percent said it was time for Republicans to just give up the fight and move on to things that are more important.
That attitude continued well into 2013: in July and in November, just for a few examples. The big question is can Republican Obamacare derangement syndrome overcome the Big Meh which has overtaken the vast majority of the country? Can they maintain their fervor when nothing really bad happens to anyone because Obamacare is now law?
Of course, their overlords, the Koch brothers have invested hundreds of millions in this fight and it would be damned hard for Republicans to just abandon it, so they won't. But the returns could be severely diminished by next November.