Howard Stern says Trump should resign

[hazard]

No we don't, it's laid out in plain language. The president's term ends at noon on Jan. 20, with no ifs, ands, or buts; at that time he is no longer the president, with the VP's office also expiring. If there is no incoming president-elect, the sequence of succession is also laid out, with the leaders of the House and Senate next in line - so if he tried it, we'd end up with President Nancy Pelosi, unless she's also up for reelection and that also didn't get done. The only crisis would be over whose job it is to send some big guys in to evict him, though my guess would be the Secret Service since they are in charge of security at the White House. I doubt there's much love lost for him there.

edit: Ninja'd!

The House of Representatives is elected for stints of 2 years for every representative, and the last task of the previous session's Speaker of the House of Representatives is to act as Speaker for the first action the House has to take after they've been sworn in by arranging the election in the House for this session's Speaker of the House.

The House is sworn in in early January, so there'd already be a Speaker for the new session of Congress by the time Trump's term lapses. This may or may not be Nancy Pelosi.

Or there was no election, in which case things get... messy.