Then you might see people voting for a third party because their vote isn't automatically wasted.
There's plenty of both sides blame that you can assign for various problems in the country, but this is not one of them, and it is incredibly disingenuous to do so.
I suspect that a lot of republican higher ups specifically avoided funding the border wall until they lost control of the house so they could manufacture this crisis (especially as the potential to fund the border wall was offered by democrats earlier and declined by republicans, and the senate passed a "just keep it open" bill before going on winter recess).
In all serious I don't know if this was meant as sarcasm but party cohesion in the republican party is quite high, it's one of the reasons the republican minority was effective against Obama - senators would freely discard logic to toe the party line.