It's a funny thing about solving problems, especially in politics. You want to solve problems, of course. You campaign on your ability to do so, and on the culpability of the other side in having created the problem in the first place.
In that respect, rarely has a problem set itself up more advantageously for the Republican Party than ObamaCare. Not a single Republican voted for it. And just about every Republican warned it would be a disaster. The public agreed, opposing the idea by large majorities before Democrats went ahead and passed it anyway in 2010.