Meadows and Ohio Rep. Jim Jordan, two of the House's most conservative members, are among the Republican leaders going to a midday White House meeting.
Trump has promised Mexico will pay for the wall, a claim Mexico rejects. McConnell told colleagues mid-Thursday afternoon that they should expect votes around noon on Friday if the House cobbles together votes for a spending bill. That measure, though, did not include any funding for the border wall, and so far, only around $1.6 billion has been allocated for President Trump's signature anti-immigration measure - enough to fix and rebuild only around 33 miles of border fence.
"This was our chance and we have blown it, unless the president were to veto it", said Huckabee.
The turn of events kick-started negotiations that had been nearly nonexistent since last week's televised meeting at the White House, when Trump neither accepted nor rejected the Democrats' offer.
In its current form, the bill only provides $1.6 billion in funding to pay for border security and other agencies at current service levels through to February 8.
Senate Majority Leader Mitch McConnell, R-Ky., said the Senate would remain in session Thursday.
Republican Sen. Richard Burr of North Carolina, a leading advocate of the conservation fund, says he and other lawmakers are working to reauthorize the program before Congress adjourns for the year.
Trump has already taken to Twitter to try to stave off a right-wing defection by simultaneously blasting Democrats and praising his own supposed border security achievements. Trump's requested $5 billion was nowhere to be seen.
Der Spiegel Admits Top Reporter Faked Stories for Years
For example, he included individuals in his stories who he had never met or spoken to, telling their stories or quoting them. The only thing that can be stated with certainty right now is that the work in uncovering that has only just begun.
Democratic leaders immediately spurned the proposal.
Pressing the case Thursday on Fox News, Meadows said: "A lot of people are very nervous this morning about whether the president will cave or not". "So that won't happen".
House conservatives have led the fight to help Trump keep his promise and fight for a wall.
But Schumer, speaking on the Senate floor on Wednesday, said the administration could not shift money around without Congress' consent. She called it a "good sign" that the White House appeared to be backing off its demands.
Because of the political gridlock, the Senate has only been able to approve a seven-week extension of existing funds. Sanders said Tuesday there are "other ways" to secure the funding. He also argued that border security is "tight" due to military and law enforcement efforts.
"The measure will provide the resources necessary to continue normal operations". It was approved by the committee in summer on a bipartisan vote. At that point, Nancy Pelosi will be Speaker, Democrats will have the majority in the House, and no bill containing border wall funding will move through the House.
More importantly, the border fencing Schumer backed in 2013 is different than how Trump has described his border wall.
At issue in the current fight is money for nine of 15 Cabinet-level departments and dozens of agencies, including the departments of Homeland Security, Transportation, Interior, Agriculture, State and Justice, as well as national parks and forests.
Pelosi meanwhile accused Republicans of having a "meltdown" over whether to pass the stopgap measure or force a shutdown. The government will partially shut down at midnight Friday unless there's a deal.