(NewsNation) — House Republican leaders are planning to bring border legislation to the House floor in May that, if passed, gives the Homeland Security secretary the power to halt all legal asylum claims if DHS deems there to be a crisis at the border.

NewsNation partner The Hill reports that the package being proposed brings together two bills: one that includes severe restrictions on asylum-seekers from the Judiciary Committee, and another from the Homeland Committee that would require completing former President Donald Trump’s border wall.

Judiciary Committee Chairman Jim Jordan, R-Ohio, confirmed to NewsNation on Thursday the controversial asylum language is included in the bill, although added that he doesn’t think current DHS Secretary Alejandro Mayorkas would use that authority.

While GOP House leadership tells NewsNation all Republicans are on board with this provision of the bill, moderates are telling a different story.

Two House members told NewsNation they still have issues with the asylum language, and can’t support the bill yet, including Florida Rep. Carlos Gimenez.

“The asylum piece is an issue for certain members like myself,” Gimenez, a Republican, said. “There can’t be a total prohibition on asylum, even when you’re full.”

At a news conference Thursday, lawmakers said they are confident that a border security package they plan to bring to the floor in just a few weeks will pass.

“We put together what we believe is the strongest immigration enforcement legislation ever,” Jordan said at the conference.

The Judiciary panel bill’s asylum proposals, according to The Hill, would allow the Department of Homeland Security to prohibit the entry of noncitizens who could present a public health threat until full “operational control” of the border is achieved. However, this proposal was criticized as it relies on a statutory definition of operational control that requires zero illegal entries of migrants and zero smuggling, which is widely seen as unrealistic.

Other parts of the bill reinstate family detention, including for minors; limits who can qualify for asylum; and raises penalties for visa overstays, per The Hill.

The Homeland Committee’s Border Reinforcement Act, meanwhile, blocks a Biden administration move that allows citizens from Nicaragua, Venezuela, Cuba and Haiti to apply for temporary entrance to the U.S. through the CBP One app from U.S. Customs and Border Patrol.

The bill would block the use of that app for anything other than commercial purposes, The Hill reported.

While The Hill notes that the legislation would represent a significant change in immigration policy, a Democratic-led Senate isn’t likely to approve it.

This all comes as Title 42, a COVID-19-era border policy, is set to end.

Title 42, which expires May 11, was a provision in the 1944 Public Health Service Act allowing the federal government to ban people from entering the country in the case of a pandemic. In March 2020, as infections began to rise from the coronavirus, the Centers for Disease Control and Prevention enacted the rule under former the Trump administration.

Officials say, though, that security will be maintained as they go back to processing migrants under Title 8.  With Title 8, those who cross the border unlawfully are subject to criminal consequences, such as deportation and a five-year ban on reentering the United States.

“Let me be clear: Our border is not open, and will not be open after May 11,” Mayorkas stressed at a news conference Thursday, where officials outlined their own plans for after Title 42.