How about an Executive Order from the POTUS saying that it is a Federal requirement that everyone must show an ID in order to vote in a National Election. To coin and old Clinton phrase: "Stroke of the pen - law of the land. Kinda cool ain't it."
They'd be stepping on the Constitution to do that. It's entirely up to the States' legislatures to determine the times, places, and manner of these federal elections, as long as they apply equally to all eligible voters. If not equal, then the courts step in.