A combination of
Nothing. Pence has absolutely no morals, principles, or shame.
and
Pence's confidence that Trump will be successfully removed form office in short order.
Why would he quit a job that he basically doesn't have to do anything and is all but guaranteed that he'll be President sometime in the next 6 years?
I meant that Pence will back Trump up until the moment when Pence thinks a successful impeachment is imminent, or that Trump can be successfully removed by the Cabinet. Then he'll do whatever he needs to put Trump down and become President.
