Republican representatives could find probably find themselves enough cover to vote for Sanders as long as they could argue that they were voting the way that their state or their district voted. If Sanders had an impressive popular vote lead nationwide, there'd be a lot of pressure on Republicans in those states to vote for him. But that would probably still make Missouri a hard get, so I think Trump would still barely pull it off.
A related and potentially more pressing question is whether the outgoing House or the new House would choose the President. Under current law, the new House would actually choose the president since the Electoral Votes aren't actually counted before congress until the new congress is sworn in in January. However, since Republicans control both houses of congress right now, they could try to pass a bill moving the date for counting the Electoral Votes up to late December, thus allowing them to choose.
Which, if it had any bearing on the outcome of the election in the House, would be filibustered in the Senate :-).
Well yes, although in an extreme scenario where it meant winning the White House, I wonder whether Senate Republicans would be willing to nuke the filibuster.
