Republicans need to take a long view. They will need to keep up their attacks on Obamacare's shortcomings but they also need to come up with a viable replacement. Obamacare may be a bad piece of legislation but it does address some real concerns like pre-existing conditions. If the Republicans don't have an answer for that then they will lose the long war.
We've already seen how efforts to replace Obamacare will play out with Social Security and Medicare. Both programs will run out of money in the foreseeable future but efforts at moderate reform have been characterized by ads showing Republicans throwing seniors over a literal cliff. Attempts to repeal Obamacare will get a similar treatment, possibly showing a mean Republican taking a crutch from a child.
That is not the end of the fight but it does make it more difficult. The left insists that Republicans are afraid of Obamacare because they know it will work. This is incorrect. What Republicans fear is that it will work for enough people to form a constituency. Just ask gun control advocates about the power of a vocal constituency.
Since the Democrats control half of Congress and the White House, there is no way for the Republicans to roll back Obamacare.
The last chance to stop Obamacare came a bit under 10 months ago. In a close election where voter turn-out was the key to winning, far to many Republicans stayed home rather than vote for a moderate/right Mormon.
The only way to stop Obamacare would have been to take the Senate and the White House. There was a good chance at taking the Senate but the Republicans lost several races against vulnerable Democrats because the Tea Party wing insisted that ideology was more important than winning.
Ted Cruz is waging a personal battle against legislation that he urged the House to pass. This is generally considered to be a stunt. For that matter, so is the House bill which has a clause that would de-fund Obamacare. That clause will be taken out in the Senate and even if it wasn't, the President would rather see the government shut down than sign a law that would de-fund his signature accomplishment.The fight to stop Obamacare was lost some time ago and, ironically, its biggest opponents killed any chance of stopping it.
They also need to follow the advice of Ronald Reagan who refused to attack fellow Republicans on ideological grounds.