The president said last week that he opposed that approach, and Senator Chuck Schumer of New York, the Democratic leader, said last month that the president would need to publicly support any funding measures before they were considered, adding that “we can’t have another situation when the president signals support at first but then reverses himself.” Mr. Trump did just that in December after the Senate passed bills to avert the shutdown, but on Friday Mr. Schumer urged Mr. McConnell from the Senate floor to intervene to end the shutdown.
Senator Chris Van Hollen of Maryland, whose state has one of the highest concentrations of federal workers, has suggested that Democrats block the consideration of all bills unrelated to opening the government until Senate Republicans allow a vote on the House bills.
Mr. Hoyer said, “I would hope that Senator McConnell would take the responsibility as the leader of the coequal branch of government, the legislative branch, and send this to the president.”
There may be added pressure on Mr. McConnell from his own ranks.
Three Senate Republicans — Susan Collins of Maine, Cory Gardner of Colorado, and Thom Tillis of North Carolina — have called for reopening the government. Two other Republican senators who have been critical of the shutdown, Lamar Alexander of Tennessee and Pat Roberts of Kansas, have announced that they will not seek re-election in 2020, so they would not face the electoral consequences of incurring Mr. Trump’s wrath.
However, some other lawmakers, like Senator Lindsey Graham, Republican of South Carolina, who is continuing to advocate a deal in which Mr. Trump would get his wall funding and Democrats would get new protections for the young immigrants known as Dreamers, view the shutdown with less urgency.
“I do want to open the government, but the goal is not to open the government. The goal is to fix a broken immigration system,” Mr. Graham said. He added later, “It was pretty clear to me that we’re never going to have a deal unless we get a wall as part of it.”
Ms. Pelosi, in her first sit-down interview on network television since reclaiming the speaker’s gavel last week, blasted Mr. Trump for suggesting that he may unilaterally move to build the border wall.