Sen. John Cornyn expressed doubts that ongoing Senate negotiations over border policy will lead to legislation that will be enacted.

“This is a very delicate and difficult negotiation,” the Texas Republican told host Shannon Bream on “Fox News Sunday.”

Cornyn suggested that even if leading Senate negotiators can reach an agreement on immigration in the coming days, other obstacles remain.

“I’ve talked to a couple of key negotiators yesterday,” he said, “and they feel like they are making some progress, but I know Senator Schumer thinks there is going to be a deal cut behind closed doors and then jam it through the Senate and then jam the House. That’s not going to happen. But we are making some progress.”

The House has adjourned for the holiday, though Senate Majority Leader Chuck Schumer has kept the Senate in session.

“We do need to be aware of the fact that this is not just an exercise in the Senate,” Cornyn said. “It’s not just the Senate and the president agreeing to something. It’s something that can actually pass the House and be signed into law.”

Regardless, Cornyn said Republicans are still seeking to push the Biden administration to handle immigration better.

“What we are asking for is humane, orderly and legal immigration,” he said.