House Speaker Nancy Pelosi, a Democrat from California, speaks during a luncheon event at the Economic Club of Washington D.C. in Washington, D.C., March 8, 2019.

The House will not take up a Senate GOP bill that could give Republicans political cover as they vote on whether to block President Donald Trump's national emergency declaration, House Speaker Nancy Pelosi said Wednesday.

By promising not to bring the legislation to the floor, Pelosi hopes to put pressure on Republican lawmakers who are trying to balance their desire to support Trump's immigration policy and their professed concerns about presidential power. Later Wednesday, Trump himself dashed hopes for one alternative that would give lawmakers more power to check future emergency declarations — but not the current one.

During a Senate Republican lunch, the president called Sen. Mike Lee, R-Utah, and said he would not back the senator's legislation to give Congress more power over emergency declarations, a Lee spokesman said. Under Lee's proposal unveiled Tuesday, national emergencies would end after 30 days if Congress does not vote to extend them. Politico first reported Trump's call to Lee.

The president declared an emergency at the southern U.S. border to secure money for his proposed border wall last month after Congress allotted less money than he wanted for the project. The Democratic-held House already passed a resolution to block Trump's declaration.

Trump has pledged to veto the House-passed bill if the Senate passes it. Neither the House nor Senate appear to have the two-thirds majority support needed to overcome his opposition.

The Senate will vote on the measure to block the emergency declaration Thursday. While five Republican senators — enough to pass the House bill in the Senate with a simple majority — have pledged to back it, some GOP lawmakers have looked for a way out of dealing an embarrassing blow to Trump.

Still, the resolution is likely to pass the Senate. In a statement cited by multiple news outlets Wednesday, Lee said he would vote to block the emergency declaration after seeing that Trump would not support his legislation.

By saying she would not bring Lee's bill to the floor, Pelosi aimed to take away an exit ramp for the GOP.

"Republican Senators are proposing new legislation to allow the President to violate the Constitution just this once in order to give themselves cover," the California Democrat said in a statement Wednesday. "The House will not take up this legislation to give President Trump a pass."

Along with Lee, Republican Sens. Susan Collins of Maine, Lisa Murkowski of Alaska, Rand Paul of Kentucky and Thom Tillis of North Carolina have also said they will vote to block the president's emergency declaration. However, Tillis "appeared to be wavering" at a weekly Senate policy lunch on Tuesday, according to The New York Times.

The resolution is set to pass even in a GOP-held chamber where Senate Majority Leader Mitch McConnell has backed the president's declaration. A Tillis spokesman did not immediately respond to a request to comment on whether the senator is reconsidering his vote.

The White House has made a late push to stop the resolution from getting through the Senate. Vice President Mike Pence met with GOP senators Tuesday to try to find an alternative path. Trump has recently tried to pressure Republicans by framing the vote as one about border security rather than executive power.

"Republican Senators are overthinking tomorrow's vote on National Emergency," he wrote in a tweet Wednesday. "It is very simply Border Security/No Crime - Should not be thought of any other way."

Trump national emergency tweet

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