President Donald Trump is scheduled to meet Wednesday with the bipartisan House Problem Solvers Caucus in the Situation Room as the White House tries to cobble together votes for a shutdown-ending bill that includes funding for his proposed southern border wall.

The Problem Solvers group is composed of just under 50 Republican and Democratic House members. The session will mark the second time in as many days the White House has attempted to court moderate and deal-minded House Democrats.

“Our hope is the same that it’s been since this conversation started, and that’s that we’ll get actual funding for real border security and the wall,” White House press secretary Sarah Huckabee Sanders told reporters Wednesday outside the West Wing. “We’re hopeful that Democrats — whether it’s the group today or leadership — will get serious about the crisis at the border.”

[Day 25 of the shutdown and the impasse held fast]

White House officials invited some House Blue Dog Democrats for a Tuesday lunch meeting with Trump and a group of House Republicans. But Democrats almost immediately blanched at the invitation, some saying Monday night that they had no intention to break bread with Trump. None showed up.

Watch: Federal worker on shutdown — ‘We can’t feed our families, we can’t live the American dream’

Democratic members are fearful of being used a pawns in Trump’s public relations strategy to try and turn public opinion over the partial shutdown in his favor as multiple polls show a majority of Americans blame him — and to a lesser degree Republican lawmakers. (Around 25 percent to 30 percent blame Democrats in various polls.)

What can GOP and Democratic Problem Solvers members expect when they, if both sides show up, get to the White House? A strong pro-wall pitch from the president and his aides. In a Wednesday morning tweet, Trump fired off stats about the effectiveness of walls without citing their sources — as he often does. (Two White House spokespersons had not responded to a request for the sources of those stats.)

There are now 77 major or significant Walls built around the world, with 45 countries planning or building Walls. Over 800 miles of Walls have been built in Europe since only 2015. They have all been recognized as close to 100% successful. Stop the crime at our Southern Border!

— Donald J. Trump (@realDonaldTrump) January 16, 2019

As Trump remains dug in on his demand for $5.7 billion for a border barrier made of “artistically designed steel slats,” Democratic leaders, as Majority Leader Steny H. Hoyer of Maryland did Tuesday, insist their caucus is “unified” against approving any wall funding.

[Frustrated by ‘my generals,’ Trump turns to ‘my actings’]

The White House appears to be employing a strategy that, should Problem Solvers Democrats and potentially others in their party invited to future such executive mansion powwows, could allow them to flip a script created last week when Trump abruptly walked out of a Situation Room meeting with Speaker Nancy Pelosi of California and Senate Minority Leader Charles E. Schumer of New York.

White House officials and Republican members who emerged from their lunch Democrats-free meeting with Trump on Tuesday painted Democrats as collectively unwilling to negotiate.

One was Rep. Clay Higgins of Louisiana, who suggested many of his Democratic colleagues are privately interested in finding a way out of the stalemate, adding: “As a body, they’ve been quite intractable.”