The president can mull whatever he wants; he doesn't have the authority to not pay.
He can mull all he wants and half the time, that mulling turns into reality.
In practice, he has the authority to do anything he wants. Who is going to stop him? You? His pets in Congress? JPow's private hit squad? Clarence Thomas?
The first rule of neo-America is that you're playing the Chairman's Game[1], and there are no more rules. Its counterparties should bargain with it accordingly.
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[1] https://en.wikipedia.org/wiki/Mao_(card_game) [2]
[2] The Chairman's Game is a game invented in a university. Some say it was invented at Stanford, while others say it was invented at MIT. It was inspired by a formerly prominent, but now somewhat disgraced Chinese politician that was famous for coming up with a lot of interesting new rules for his subjects to follow, and enforcing those rules very harshly, without necessarily informing those subjects what those rules were. It's a little bit like Uno, a little bit like Crazy Eights, and the only thing that I can tell you about it is that there are times, when playing this game, when it is not a good idea to speak.
What a ridiculous statement given everything we've seen in the last year. The president doesn't have the authority to withhold funding to the states, or to deploy the national guard (absent an emergency), or to use the Justice Department as his personal law firm, and yet... All he needs to do is have the appropriate person fail to do their job and nothing gets paid.