Can you just imagine all the red-faced screams of "Fascist!" "Dictator!" "Tyrant!" etc. if it were a Republican in the White House keeping reporters away like that?

I may be mistaken, but I believe that the whole point of the "deem and pass" trick is that the Senate bill as is won't be "deemed" to have passed UNLESS the Senate passes the reconciliation bill. That's why the (reports of) the Senate parliamentarian's opinion that the Senate could not consider the reconciliation bill until the original bill had been signed into law is thought to be an insuperable stumbling block to the "deem and pass" chicanery.