He'd need a majority of the Senate to go along with whatever rule change or rule interpretation had that effect. Given that budget and reconcilliation are done without filibuster, I see no reason that a CR couldn't be deemed to be in the same sort of bucket. Clean CR, no cloture, max xx hours of debate and vote.
The GOP must believe this shutdown benefits them politically.
That's what I'm thinking. Leave it shut down until the parasites start going ape-$h!+ ballistic on the RAT Senators.