Senate lawmakers have formed a new bipartisan “gang” to try to resolve the impasse over border wall funding that has caused the longest government shutdown in history.

The group includes 20 Senate lawmakers — 10 Republicans and 10 Democrats — according to Sen. John Cornyn, R-Texas. Cornyn is not in the gang but is a member of the GOP leadership team and has been briefed on the discussions so far.

“My hypothesis is when federal employees start missing their paychecks, that changes the picture,” Cornyn said. “A lot more Senate Democrats are under pressure. If people start breaking off, maybe there is a chance to end the impasse.”

Cornyn said he also talked to “a senior Senate Democrat about some ideas of what we could do,” but he added a proposal would ultimately have to meet President Trump’s demand for border wall funding, which Speaker Nancy Pelosi, D-Calif., and Minority Leader Chuck Schumer, D-N.Y., have so far refused.

“I”m glad they are talking, but no real progress yet, other than talking,” Cornyn said, referring to the gang.

It's been nearly six years since the Gang of Eight organized an immigration bill that envisioned a path to citizenship for illegal immigrants in exchange for tougher border security measures and language aimed at ensuring immigrants don't overstay their visas. The Gang of Eight bill passed in a 68-32 vote in the Senate, but it was never taken up in the Republican-led House.

The new "gang" consists of 20 percent of the Senate and is hoping to find some kind of answer on immigration that allows the government shutdown to end. Getting there will likely involve some agreement to fund a border wall, a demand of President Trump's, and some kind of tradeoff that Democrats can support.

Sen. Thom Tillis, R-N.C., is a member of the gang but refused to confirm how many are in it, other than to say several lawmakers are involved and talks are bipartisan.

“We are just trying to get the members to talk about a way we can work out of it,” Tillis said. “It's good that we’ve got Democrats and Republicans in the room. The real question is, can we come up with something that makes progress on border security funding and things that are priorities for my Democratic colleagues.”

The group began meeting Monday as the government shutdown dragged into a fourth week. The partial closure has hobbled federal agencies and departments and has left 800,000 federal workers without pay as of Friday.

House Democrats on Tuesday will offer a bill to fund government operations until Feb. 1. On Thursday, they’ll take up another measure that would fund the government until Feb. 28. But Republicans are expected to hold firm against these ideas because they don't address the border wall.

When asked whether the GOP-led Senate would be tempted to take up the House-passed proposals to temporarily re-open the government, Cornyn said, “No.”

Cornyn and other Republicans believe Democrats are to blame for the stalled negotiations with Trump by refusing to back any money for a border wall.

“Somebody’s got to move,” Tillis said. “And we are trying to help them.”

The new gang comes days after a group of Senate Republicans failed to get a deal going that would trade legalization of Dreamers for border wall funding. The deal stalled because Trump is refusing to give up leverage by agreeing to open the government first, without a firm guarantee that wall funding will be on the table in a future immigration deal.

Tillis and Cornyn said they believe the only way to get Trump to sign spending bills that end the shutdown is to secure a deal first that trades off border security and a wall for something Democrats want, such as legalizing Dreamers.

“Obviously there has to be something in it for border security, some portion of that for a wall,” Tillis said. “In order to do that, we have to make progress on a broader immigration deal.”

Tillis suggested such a deal should not be too broad, or it would shed support on both sides and fall apart.

Sen. Shelley Moore Capito, R-W.Va., who chairs the appropriations subcommittee overseeing border security, said any solution produced by the gang has to be bipartisan.

“It will be interesting to see where it goes,” Capito said.

Senate Appropriations Committee Chairman Richard Shelby, R-Ala., said lawmakers “ought to stop blaming each other" and said it's time for Democrats to explain what could make them say "yes."

“What do the Democrats really want? We don’t know,” Shelby said. “If they just want to be against Trump and Trump’s idea of a wall, that is not going to go anywhere I don’t believe. What do they really want? There has to be something, to give and take. On any negotiation.”

A small group of Senate Republicans want to reopen the government now, while lawmakers are negotiating a deal on border security.

Sen. Lindsey Graham, R-S.C., who is included in the bipartisan talks, asked Trump if he would agree to sign a temporary spending bill while Congress considers an immigration and border security deal. Trump declined, noting that Democrats have pledged to block any wall funding, now or in the future.

Sen. Lamar Alexander, R-Tenn., suggested that the Senate could pass a bipartisan deal.

“Sen. Graham has made a perfectly logical suggestion,” said Alexander. “What I would hope is that the president would reconsider. I still think that’s the best idea.”