Speaker Nancy Pelosi said Thursday the House will not take up a new Senate GOP bill to curb the National Emergencies Act, saying her goal is to constrain President Trump, not to tackle the bigger presidential powers issues.

“Republican senators are proposing new legislation to allow the president to violate the Constitution just this once in order to give themselves cover,” she said. “The House will not take up this legislation to give President Trump a pass.”

She was referring to a new bill by Sen. Mike Lee that would, in the future, limit a president’s powers under the 1976 Emergencies Act. The bill would not apply retroactively to Mr. Trump’s recent border emergency declaration, nor to the more than two dozen other emergencies still in effect from previous presidents.

Democrats say the GOP is using the Lee bill as political cover so they can vote to back Mr. Trump’s wall declaration, then cleanse themselves by voting to prevent repeats in the future.

Senators face a showdown vote on Thursday on the wall declaration.

The House already passed a resolution to overturn the declaration, and enough Republicans appear ready to join Democrats in the Senate to approve it in that chamber, too.

Mr. Trump has vowed to veto the bill, and there is not enough support right now to override him.

Senate Majority Leader Mitch McConnell told reporters on Tuesday that Republicans don’t question Mr. Trump’s powers, but do have misgivings about his decision to siphon funds from the Pentagon to pay for extra border wall construction.