Pelosi and other House Democrats have argued that Trump's emergency declaration, which he is using as a way to spend more on barriers at the border than Congress has authorized, violates the Constitution.
If Trump commits to signing legislation handcuffing future emergency declarations, more GOP senators might vote Thursday against a separate bill blocking his border emergency.
At stake are billions of dollars in funding for a wall along the U.S. -Mexico border that Trump is demanding but Congress has refused to fully provide.
Barring a last-minute deal on some other face-saving measure, up to a dozen Republicans could join all Senate Democrats in voting to send the disapproval resolution to Trump's desk, setting up the first veto of his presidency. Congress can vote to block an emergency declaration, but the two-thirds majorities required to overcome presidential vetoes make it hard for lawmakers to prevail.
Vice President Mike Pence met with Republican senators this week to push Lee's plan, saying Trump would support it. "While we have impeachment authority, we need to be very cognizant of what the American people believe, and I agree with the speaker, that the probability of success is low, and the distraction would be major". The White House nonetheless views the chaos as a mess of senators' own making, one senior administration official said.
PM: Will not allow Pakistani soil to be used for terrorism
Meanwhile Pakistani officials maintain the crackdown is part of a long-planned drive and not a response to Indian anger. Pakistani Prime Minister Imran Khan's government began a crackdown against Islamist militant organisations.
The White House wants to extend the 30-day period, perhaps to 30 days when Congress is in session, said one GOP aide familiar with the discussion who spoke on condition of anonymity to describe closed-door talks.
GOP Sens. Mike Lee of Utah and Todd Young of IN were also IN discussions with the White House about related legislation that would curb the ability of future presidents to declare national emergencies. "I will be voting to terminate the latest emergency declaration".
Republicans have also voiced concerns about the precedent that could be set for future Democratic presidents to declare national emergencies on any number of issues. It would apply to future emergencies, not Trump's current border emergency.
Under the emergency declaration Trump signed on February 15, he would take money from other federal programs to build the barrier he says is needed to curb illegal immigration and the flow of illicit drugs.
In New York, federal prosecutors are examining the president's role in hush-money payments shortly before the election to porn star Stormy Daniels and Playboy model Karen McDougal to keep them quiet about affairs they said they had with Trump.
The White House says that Trump is within his rights to declare the national emergency and that opposing him will be seen as a vote against border security - which could play poorly in their home states.