In general, being on the losing side of any vote does not result in political consequences.
So there will not be political consequences towards Heitkamp over the Kavanaugh vote.
No, there will be consequences, it just means it wont be blaring that "SHE DECIDED KAVANAUGH WOULD FAIL!" Really, the way for Heidi to win at this point is to control the airwaves, get people knocking on doors as quick as possible, and hope that Kavanaugh fades into the darkness, and something like tariffs comes back.
Still though, unless polling shows otherwise, she aint favored at all.