“It simply sends a message that Congress is going to stand up for its institutional prerogatives and abide by the separation-of-powers framework that was carefully worked out by the framers in the Constitution,” Ms. Collins said on Monday. “I truly don’t see this as sending a message at all one way or the other about border security but rather about executive overreach.”

Ross K. Baker, a political scientist and expert on Congress at Rutgers University, said passage of the resolution would amount to a “serious rebuke” of the president.

“It’s Congress saying: ‘This has gone far enough. We’re not going to roll over and play dead for the president,’” Mr. Baker said. “It’s the kind of thing that James Madison had in mind when he laid out in the Federalist Papers the argument for separation of powers and checks and balances.”