Sen. James Lankford, R-Okla., on Sunday said a deal on immigration and border policy could be reached this week.

Lankford, who has been leading negotiations for Senate Republicans on border policy, said in an interview on “Fox News Sunday” that border negotiators are “hoping to get text out by later on this week.”

“Everybody will have time to be able to read and go through it. No one’s going to be jammed in this process,” Lankford said.

Lankford, alongside Sens. Chris Murphy, D-Conn., and Kyrsten Sinema, I-Ariz., have held discussions in recent weeks to reach an agreement on toughening asylum laws. House Republicans have demanded new restrictions on migration in order to secure their support for new aid to Ukraine in its war against Russia.

“It’s a matter of trying to be able to get this out,” Lankford said. “But to make law, we’ve got to have a Democrat Senate, a Democratic White House and a Republican House to be able to go through this. So this agreement has to work. Everyone’s counting on this actually working.”

The Senate negotiators met for more than three hours in the Capitol building on Friday working on coming to a consensus on any remaining sticking points before members return this week from winter recess.

That meeting came after House Speaker Mike Johnson, R-La., and dozens of House Republicans visited the southern border in Texas last week to bring attention to record migrant crossings and criticize the Biden administration’s immigration policy. Their trip fueled threats by right-wing Republicans to shut down the government in the coming weeks unless President Joe Biden and Democrats agree on imposing stricter border laws.

Johnson and other GOP leaders, however, have not endorsed threats of a shutdown coming from the most right-leaning House members. In a separate interview on CBS’ “Face the Nation,” Johnson said that he thinks Congress “may be close to a deal” on top-line numbers to avoid a shutdown in the coming weeks and that he has not seen the text of what Senate negotiators are working on.

In his interview on “Fox News Sunday,” Lankford indicated that he is open to Johnson sitting down with the White House directly to reach an agreement on border policy and that the House could make its own changes to a Senate-passed bill. (If the House did make changes, the Senate would need to agree to them as well to send a bill to Biden’s desk to become law.)

“If we can pass this in the days ahead in the Senate and send it over to the House, the House can work to improve it or the House can take a serious look at it and say, ‘Look, this makes real progress on the border, let’s go get this, bank this and then keep going for more,’” Lankford said.

Johnson, on CBS, reiterated that the House is “insisting upon the provisions of H.R. 2,” a Republican-led border bill that passed the chamber along party lines.

Asked if he’ll commit to bringing a Senate deal to the House floor, Johnson replied, “It’s a hypothetical question.”

Pressed on whether he wants a deal, Johnson said, “Of course we want a deal.”

“We want to solve this crisis,” he said. “We have to — we have a moral obligation to do so.”