That would be fantastic if it happened, but let's be honest here; The GOP, Congress, and Senate are politicians. There is no way in hell they are just going to say, OK your Shut Down for this duration while we sort some shit out. That would be too much like actual work/problem solving.
Anything of the sort would have to be some sort of emergency power from the Office of the President.
Most likely we will just see the EBS put into play while Social Media plays out its Clown Show…