More seriously: if he refuses to leave the White House on 20th January, he is not still President, is he? And Pence is no longer Vice-President. That is the case unless they win fairly thoroughly: his term of office ends on that day and unless he is re-inaugurated, he is no longer President, no matter what law-suits he may be trying to pursue.
Who is then in charge? Nancy Pelosi? She doesn't move into the White House, I assume, but does she take over running the country until the mess is sorted out?
Oh, and is a vote for Trump also a vote for Pence, or is it possible to end up with the President from one party and the Vice President from the other?