The first thing the GOP needs to do viz. Obamacare is to come up with a reasonably well-developed alternative. The fact of the matter is, Obamacare didn't spring up unbidden to spoil an otherwise perfectly pleasant party; it gained traction because there were serious problems with the health care system in the US and when it was introduced it was basically the only comprehensive "solution" on offer.
The GOP will not find a lot of support for repealing Obamacare unless it has something else to offer in its place, something that addresses the dysfunction that existed prior to Obamacare, as well as the new problems created by Obamacare. Right now the GOP is simply going with the negative - anti-Obamacare - and that simply leaves it open to the accusation that all the GOP cares about is going back to the bad old days.
The fact of the matter is this: for at least the next two years the GOP cannot repeal Obamacare, or even substantial portions of it, because Obuttocks will veto each and every such bill. That being said, the creative way to respond to that is to use the next two years to start running positive alternatives to Obamacare up the flagpole to see what Americans think about those various alternatives. Start passing bills that affirmatively address the problems that existed before Obamacare, not just bills that repeal Obamacare, so that the GOP can start presenting various aspects of an affirmative replacement for Obamacare now to gauge how Americans will react, with the comfort of knowing that the GOP won't have to commit to something that turns out to be a dud because Obama will dutifully veto whatever the GOP sends to his desk for signature.