It's simple, they dug themself into a corner. Obama listens to them, he gets credit for being a unifier (as he promised), Obama incorporates their ideas, he gets credit for it (for improving the healthcare). Since Republicans have decided to stonewall anything as thier main strategy, even at the cost of the American people (a failed bill will stop a reform for at least a decade), they cannot stop doing it without giving tribute to Obama. Since being obtrusive works and they don't have a decent alternative, they'll keep doing it until it starts to backfire.
A strong Republican leader might be able to get a decent credit for normalizing the US politics, but they don't seem to have one, so the tribute would go to Obama.