Some measures have better chances than others. As momentum appeared to be evaporating last week to pass the criminal justice bill, it received a lift on Friday, when Mr. Trump pressured Senator Mitch McConnell of Kentucky, the majority leader who has resisted scheduling it for a vote, to “Go for it Mitch!” Senator Ted Cruz of Texas, a prominent Republican holdout, also endorsed the measure, bolstering proponents’ argument that the bill has substantial enough support to pass.

Senators are also poised this week to take action on a resolution to cut off American support for the Saudi-led war in Yemen, a rebuke to Crown Prince Mohammed bin Salman of Saudi Arabia for the killing of Mr. Khashoggi and to Mr. Trump for failing to hold him responsible for it. While there is substantial bipartisan support for the move in the Senate, it faces a roadblock in the House, and Mr. Trump would likely veto it. And it is not clear whether the measure or other proposals to punish Saudi Arabia — by imposing sanctions or a weapons ban, or condemning the crown prince directly — could be attached to the spending legislation.

“The fewer things we put on the approps bills, the better chance of passing,” Senator Richard C. Shelby of Alabama, the Republican chairman of the Senate Appropriations Committee, told reporters last week. “I’d rather deal with appropriations, for the most part, and keep legislation off anywhere I can.”

Five out of the 12 annual spending bills have already been passed, leaving seven to complete by Dec. 21, though those are expected to be rolled into one package. Negotiations over the Homeland Security bill, the most contentious of the group, have essentially paused as both chambers wait to see the outcome of the Tuesday meeting between Mr. Trump, Ms. Pelosi and Mr. Schumer.