Keep in mind that it was Nixon's nomination of Gerald Ford (to replace former VP Spiro Agnew who had resigned) that largely cleared the way for pushing for Nixon's impeachment, since Ford was acceptable to all sides in case he had to himself become president.
And this is actually a very serious question, since it's possible that any Pence removal from office -- remote as that is (though not implausible) -- would probably not take place until well-down the line, most likely after the 2018 mid-term elections...at which point it is not unreasonable to think that Nancy Pelosi will again be Speaker of the House, and next in line to be president if Pence doesn't name someone as his VP -- who is acceptable to Democrats. He couldn't name an ideologue like himself, since the Democrats could block the person, leaving the door open to Pelosi. And honestly, I don't think Democrats would actually want that, since a change of party in the White House without election would be deeply problematic. But it still gives them great power in making sure Pence would name someone reasonable that Democrats could accept. Someone who would be sane and solid, but not necessarily a threat in 2020.