Senate Majority Whip John Cornyn, R-Texas, suggested Wednesday that if Democrats want a permanent solution for the Deferred Action for Childhood Arrivals program, Republicans will want something close to a 10-year appropriation for a U.S.-Mexico border wall and security funding.

“If you want an annual appropriation, then I think you’ll get a one-year extension of the DACA status,” Cornyn said. “I think it’s not a good solution to say we’re going to provide a permanent solution for the DACA recipients and yet just do a one-year appropriation and then maybe an authorization, which may or may not get funded.”

Cornyn said the longer appropriation, which he would prefer last 10 years, could be placed in a trust fund or something similar. “I don’t think anybody believes that you can rely on just an authorization,” Cornyn said.

The White House over the weekend expressed similar concerns that a future Congress could de-fund construction of a wall or other type of physical barriers if President Donald Trump’s request for an $18 billion appropriation is not honored.

“We don’t want to be playing games. We want to find a way to make sure that physical barrier is built,” White House legislative affairs director Marc Short told reporters at the Capitol Sunday night, as lawmakers tried to work their way out of the partial government shutdown. “As you’ve heard the president say, ‘I’m not asking for 2,500 miles. I’m not asking [to build] a concrete wall. I’ve accepted CBP saying that in many cases a porous wall is what’s better for security.’”

Short said if Congress considered a multiyear appropriation inappropriate, “then let’s give us a one-year, $18 billion appropriation and we’ll find a way to make that work.”

Senate Democratic Leader Charles E. Schumer of New Year said over the weekend that he had offered even more money than Trump requested during a meeting Friday with the president. But Schumer on Tuesday said he’d taken his offer off the table, scrambling the contours of a wall-for-Dreamers trade that had been under discussion.

Talks are starting anew, however, because the current stopgap funding bill Trump signed into law Monday night lapses on Feb. 8. In an attempt to reach agreement on a fix for the DACA program, which will determine whether about 700,000 undocumented immigrants brought to the country illegally as children could be exposed to deportation, Cornyn said he and Senate Democratic Whip Richard J. Durbin of Illinois would be meeting with a group of roughly 20 senators around 5 p.m. today.

GOP Sens. Susan Collins of Maine and Lindsey Graham of South Carolina “were in charge of inviting the attendees and last thing I heard there are going to be 10 Republicans and 10 Democrats,” Cornyn said.

“Sen. Durbin and I are tasked with the job of being sort of the clearinghouse for ideas, so we can build from the bottom up a plan that hopefully can get enough support that we can get passed. But, it’ll also have to get the president’s support eventually. Without his support, I don’t think it’ll pass the House of Representatives and I don’t think obviously he would sign it,” the No. 2 Senate GOP leader said.

Cornyn said the border wall design will be left up to the Department of Homeland Security, but he expects it would be a combination of infrastructure, technology and personnel.

Cornyn said he assumed that a final DACA bill wouldn’t go through the Judiciary Committee, but would be agreed to by a bipartisan group of legislators and then go directly to the Senate floor. He said Judiciary Chairman Charles E. Grassley, R-Iowa, would have to agree that’s an acceptable process.

Cornyn also indicated that final bill won’t be associated with any particular duo or group of senators in the way a Graham-Durbin bill (S 1615) to legalize Dreamers or a proposal they reached with four other senators is linked to the senators from South Carolina and Illinois.

“I told Sen. Graham yesterday, I said ‘All of us have a little bit of baggage when it comes to the immigration issue and people react sometimes to, well a Graham-Durbin bill.’ That sends signals when they are tied to different personalities,” Cornyn said. “So, what we need to do is disassociate the personalities from the policy and then hopefully being to build the policy in a way that is personality neutral and helps us build consensus.”

Niels Lesniewski and Dean DeChiaro contributed to this report.