Most Republicans in Congress, including those leaders who will also be in the meeting with the president, have backed the president, though there were signs of a fraying alliance as two vulnerable senators from Democratic-leaning states, Cory Gardner of Colorado and Susan Collins of Maine, expressed misgivings over their leaders’ intransigence. Mr. Gardner called on his party to end the shutdown, even if it meant not funding the wall, and Ms. Collins said she would support measures to fund the government in already approved appropriations bills.
Sean Hannity, a Fox News commentator close to Mr. Trump, may have signaled a way out, when he suggested on his program Thursday night that the president resurrect the old Democratic notion of twinning wall funding and protecting from deportation young immigrants brought illegally to the country as children, so-called Dreamers.
Such immigrants are currently protected by DACA, the program created by President Barack Obama, but Democrats would likely want something more, the DREAM Act, which would protect young immigrants by statute and offer them a path to citizenship.
A compromise linking the Dreamers to the wall has been floated by Senators Lindsey Graham, Republican of South Carolina, and Lamar Alexander, Republican of Tennessee.
Newsmax, another media outlet favored by the president, reported that Mr. Hannity explicitly said Mr. Trump was now willing to negotiate the fate of the Dreamers to secure his wall.
But Mr. Trump is also facing pressure from his base to deliver on the wall, a central promise of his presidential campaign. Mr. Graham said Wednesday in an interview on Fox News that Mr. Trump’s presidency could effectively be ended if he abandoned the wall pledge. And the president this week rejected the “Dreamers for wall” idea.
On Thursday, Mr. Trump made a dramatic appearance in the White House Briefing Room, his first as president, trying to press his case for the wall by asking border agents to outline the threats posed by illegal immigration. But he simply reiterated his position and took no questions.