I can’t recall offhand what the rules are for adjourning the Senate.
But I’m guessing there are procedural ways to start mucking things up. Repeated quorum calls that require the Dema to maintain a floor majority at all times, opposing unanamous consent to make everthing a rollcall vote, raising lots of points of order, personal priv, etc to just suck up time.
Then start filing motions to adjourn. See how long it takes Dems to start voting in support.
I do know one thing. The new Congress takes office at 12pm January 3rd.
Until then the lame duck Senate could theoretically stay in session as long as a majority is present.