What's most likely to happen: They'll get most of the nominations confirmed, Thune will Recess the Senate, and all of the remaining picks will be appointed during the Recess - and Trump will effectively have 2 years to get the cleaning done.
But what if Thune were to refuse to go into Recess to give someone like Gaetz a Recess Appointment?
The Constitution gives the President the power to adjourn Congress:
Quote:
he may, on extraordinary Occasions, convene both Houses, or either of them, and in Case of Disagreement between them, with Respect to the Time of Adjournment, he may adjourn them to such Time as he shall think proper;
Even if Thune won't go into recess, all he needs is for Mike Johnson to demand adjournment for 10 days. Trump can then adjourn both, appoint his cabinet, and get to work for up to 2 years.
This has never been done by a President. But I think it's on the table. Trump isn't playing games and he isn't going to be beaten right on these things.
The ramifications would be huge - and I'm sure the Supreme Court would get involved - but the clause is pretty clear here. Heads would absolutely explode in DC and Cable News - which would be fun to watch.