Nothing. Obama can use the power of an executive order, but I think it would be best for the Democrats long term interests to just wait out the next two years until President Clinton and the Democratic Senate (I know I have been a dick tonight, but I know that the Republican Majority doesn't survive 2016...) can finish off the job.
I'd advise Obama to give up on immigration reform and just keep stalling GOP attempts to repeal Obamacare. At the end of the day, his legacy will be healthcare and he should fight hard to keep that victory instead of bowing to moderate heroism.
But if he does let them repeal Obamacare, Democrats can run for the next 2-4 (or more) election cycles pointing to every flaw in the health care system and claim "that only exists because the Republicans repealed Obamacare!" (But why would they do that? It's a Republican, pro-corporate plan. Get rid of Obamacare and you're giving the chances of a real national health care system a huge boost!)
