Honestly? Not a whole lot. The president doesn't really have much power. I think we'd see the most vetoes in history, and he might rescind some Executive Orders, but it's really Congress that has all the power and they are too in love with themselves to ever give up an ounce of it.
"Ah, you miserable creatures! You who think that you are so great! You who judge humanity to be so small! You who wish to reform everything! Why don't you reform yourselves? That task would be sufficient enough."
-Frederick Bastiat
-Frederick Bastiat