Look at the Scottish independence referendum in 2014. It failed to win a majority, and even if they had won a narrow majority, who's to say what would have happened. But if 60 or 65 percent had voted for independence, clearly that would've happened. Some limited numbers of the no-voters might have decided to relocate to elsewhere in Britain because they held that strongly to their beliefs, but the rest probably would've just had to resign themselves to life in independent Scotland and being split off from the rest of Britain.
It would be similar if it ever came to the US splitting up - in clearly blue or red states where two thirds of the population votes one way or the other, the minority would have to resign themselves to what happened, eventually aligning themselves politically with the moderates on the other side and creating a new political balance that way, or alternatively relocate if they felt strongly enough about their beliefs - or threatened enough.
And you know, there have been talks of California splitting off, for instance - of course that movement is a joke with zero support today, but it needn't stay that way forever.