It's been proven that the Republicans will fiercely oppose anything Obama wants so in order to get things done I suggest he start saying he wants the opposite of what he really wants then sit back and let the GOP fight to get them done.
For example, he could come out strongly against global warming and say he believes it's a hoax then the right will declare it the most urgent matter ever and make it their latest cause.
Or maybe even be a little more bold and announce that rich people deserve to pay no taxes then watch the Republicans demand that the rich be taxed more than anyone has ever been.