In this interview with NewsMax, Republican presidential candidate Ben Carson was asked what he would do to preserve traditional marriage if the Supreme Court were to recognize marriage equality nationwide. He said this:
First of all, we have to understand how the Constitution works, the president is required to carry out the laws of the land, the laws of the land come from the legislative branch. So if the legislative branch creates a law or changes a law, the executive branch has a responsibly to carry it out. It doesn’t say they have the responsibility to carry out a judicial law. And that’s something we need to talk about.
Now it's possible that Carson was trying to say that if the Supreme Court were to "legislate from the bench" and make an unconstitutional order, then the President would have no obligation to execute it.
But assuming he meant all judicial orders, lawful or otherwise, my question is, what is the executive branch's responsibility in executing judicial orders? I've heard of the (likely apocryphal) story of Andrew Jackson hearing a Supreme Court order forbidding him from displacing Native Americans from their land, and responding with the suggestion that if the Chief Justice passed the order, then he can enforce it himself. But what does case law say about whether the President can neglect to enforce a lawful order from a Court?