One Democrat, Senator Patty Murray of Washington, introduced separate legislation that would restrict the president from reallocating congressionally approved funds, though it is unlikely to reach the floor.

Most of the spending bills containing those provisions came out of the Senate Appropriations Committee on strictly partisan lines, and the White House has held firm that Mr. Trump is unwilling to accept anything less than the $5 billion he has requested for wall construction. (Democrats have said that such a demand is a nonstarter.)

The Senate is expected to vote in the coming days on bipartisan spending bills that would fund some domestic programs, considered to be a promising start by several lawmakers.

Senator Mitch McConnell of Kentucky, the majority leader, on Monday urged his colleagues to move forward with procedural votes on defense funding, once some of the domestic bills had passed. But his Democratic counterpart, Senator Chuck Schumer of New York, has previously objected to legislation that was not bipartisan, warning that “that’s what the history of this chamber shows.”

But even if the Senate approves the legislation, for any federal programs to be permanently funded, senators must reconcile their legislation with the House’s version of the bills — and secure Mr. Trump’s signature.

“Barring a miracle of the first order up here, I don’t see any way,” Senator Richard C. Shelby, Republican of Alabama and chairman of the Senate Appropriations Committee, said of the possibility that any of the spending legislation becomes law before Nov . 21. “Based on my experience here, I could see it going into late January, February. Might not. I hope it won’t.”

Standing in the Capitol late last week, he waved his hand in the direction of the House chamber. “We have things coming from the House, looming on the horizon. That’s going to take time in the Senate.”