BTW, I just learned yesterday that the way the Democrats can postpone a vote on Senate rules for 2 or 3 weeks and still have that vote on "the first day of the new Senate" is that a "day" for the US Senate consists of the time between the opening and closing gavels of that "day."

So if the President of the Senate (the Vice President) calls the Senate into session, the Senate can take a "recess" of indeterminate length before the closing gavel is pounded.   In this case, they've decided not to end that recess and continue the "opening day" session until sometime after the MLK JR holiday.