House Appropriations Committee spokesman Evan Hollander said in a statement that Democrats want the figure to be less than $2 billion.
Congress has until February 15 to approve an agreement before the government runs out of money.
Republicans offered mixed views on whether a deal can be done by Friday.
Alabama Republican Sen. Richard Shelby, West Virginia Sen.
"At such time as we overcome Trump obstacles and secure the returns, there needs to be a careful, objective review of them in private", Doggett said.
Even with a deal, it was possible Trump might try using claims of executive powers to reach for more wall funding, sparking more fights with Congress.
Congressional leaders in December reached a deal to keep the government open, which the Senate approved by unanimous consent. Democrats have rejected building a wall, though Lowey said that additional fencing is part of the talks.
On Capitol Hill, House and Senate conferees were nearing an agreement that could offer the president between $1.3 billion and around $2 billion in funding for border security, a range, still subject to change, that could include some physical barriers and result in a deal as early as Monday.
During their meeting, lawmakers heard from Border Patrol and customs officials who sought to justify spending the $5.7 billion demanded by Trump on a border wall, Durbin said. Border apprehension data from December 2018 reveal that the number of adults traveling to the southern border with children has skyrocketed by 280 percent compared to the same time previous year. But, he added, "It would be in my opinion right that we know where the president stands before we vote on this".
Rep. Lucille Roybal-Allard, D-Calif., a negotiator, said it was "unrealistic" to think there would be no funding for physical barriers. "I understand his strong-felt beliefs on that, but I don't think anybody at this point in time is going to bring something in that might be a deal-breaker on either side when we're so close". "We will not be bullied by the president of the United States", Jeffries said.
While Trump repeatedly has described illegal immigration as "an urgent national crisis", Durbin said the focus at Wednesday's briefing was on "the most serious drug epidemic in the history of the United States of America" with undetected opioids coming mainly through USA ports of entry.
The chairman of the House Ways and Means Committee has said he plans to request Trump's returns using IRS code 6103, a provision that Democrats say allows the chairman of the House Ways and Means committee to request Trump's tax returns.
All of this is good news, of course, and it seems to be yet another sign that Republicans on Capitol Hill most definitely don't want to see a replay of the five-week shutdown that paralyzed the government and much of Washington from December 22nd until almost the end of January. But the president has gotten increasing pushback from other members of his party.
Members of both parties have expressed opposition to Trump bypassing Congress by declaring a national emergency at the border, a move that would be certain to produce lawsuits that could block the money. But any lawmaker could demand a vote on overturning the president's decision, setting up a test of the president's power and his pull within the GOP.
Some of the witnesses - a crew of tax and ethics experts - have urged Congress to demand them, arguing that it would provide answers to whether the President, who has maintained ownership of his business, is benefiting from public office.
Rep. Mark Meadows, R-N.C., who leads the hard-right House Freedom Caucus, said he spoke Thursday night to Trump, who he said was in "wait and see" mode. Democratic presidential nominee Hillary Clinton said during the 2016 race.
He said the White House had already identified "substantially more than $5.7 billion" that could be redirected for these purposes.
"I have asked the administration to be as noninterventionist as I am on that", Pelosi told reporters Thursday morning.
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