Republicans will side with anyone they have to in order to hurt Democrats and ensure a disaster happens on their watch. It's all cynicism. If this potential strike was happening under Trump, these same Republicans would be calling for the return of the Pinkertons.
It would be a bit more complicated than that. House and Senate Republican leaders would both want to respond like Reagan did to the air traffic controllers, but then Trump would suddenly tweet out in the middle of the morning that he will be vetoing any deal that doesn't have a week of paid sick leave "for our great patriotic railroaders." I think Trump would narrowly win this and flip just enough Republican votes.