There is no COnstitutional provision for such a suspension. Lincoln suspended the 14th Amendment for the duration but he did not suspend elections. I suppose a president could do that but the opposition would cancel out any benefits. He would only do it if he really were bent on doing the Caesar thing. That is not so likely in this society as in, say, Rome because the military is not personally loyal to him. In Rome the army was raised and personally loyal to its commander. Wars were actually run on a sort of free enterprise model during the Republic.
TYPO POLICE:
Which showed how great Lincoln's power was considering that Lincoln was dead when the 14th Amendment was ratified. ;-)
You meant, of course, habeas corpus.