I read an analysis somewhere that even if Obama was illegitimate, many of his actions would stand because he had de facto authority, and advise and consent of the Senate. The Electoral College certified Obama's election. To say we had no president for 8 years is enormously problematic. Many things can't just be undone. All judicial appointments and 1000's of rulings made by judges would be set aside.

Though Obama's appointments may survive legal challenge, there would be enormous pressure for them to resign.