WASHINGTON — After Speaker Mike Johnson rejected a Senate-passed national security package, centrist House Republican lawmakers said Thursday they will soon unveil their own bipartisan proposal that calls for new border policies coupled with critical military aid for Ukraine, Israel and Taiwan.

“This is a really good piece of legislation. It’s pared-down. It’s airtight. There’s really not a whole lot of area that anyone can criticize on this,” said Rep. Brian Fitzpatrick, R-Pa., though the group has yet to release the text. “And it’s bipartisan. It’s the only bipartisan solution in the House.”

The bipartisan package will initially have eight co-sponsors, equally split between Democrats and Republicans. In addition to Fitzpatrick, the Republican backers are Reps. Don Bacon of Nebraska, Mike Lawler of New York and Lori Michelle Chavez-DeRemer of Oregon, a lawmaker confirmed.

The Democrats are Reps. Jared Golden of Maine, Ed Case of Hawaii, Marie Gluesenkamp Pérez of Washington and Jim Costa of California, the lawmaker said.

Punchbowl first reported the list of co-sponsors.

Fitzpatrick is a co-chair of the Problem Solvers Caucus, a bipartisan group of centrist lawmakers, but he said the legislation wasn’t a Problem Solvers product.

Bacon, a swing district lawmaker, said he worked with Fitzpatrick to craft the bill and hopes to release it soon. In addition to scaled-back aid for Ukraine, Israel and Taiwan, the package borrows language from the House GOP’s tough border bill, known as H.R. 2, members said.

That includes language relating to the “Remain in Mexico” policy that required some asylum-seekers to wait in Mexico while their claims were adjudicated. President Joe Biden ended the policy, which human rights groups said led migrants to face kidnappings and violence, when he took office, and the Supreme Court upheld the move.

“It’s going to be military aid only — Ukraine, Taiwan, Israel. And the Remain in Mexico policy using a lot of the wording from the H.R. 2. And we have Democrat buy-in,” Bacon said. “And I think this is a good spot to be if you’re Republican. You’re reducing the Senate bill by about 30%. So it’s fiscally more responsible. We know we got to do military aid to Ukraine or they’re going to fall, and it’ll cost us more if that happens. And we can deal with the border. So I just feel good about what we’re doing.”

But reinstating the border policy would require cooperation from Mexico, which it has rejected. Neither Fitzpatrick nor Bacon could explain how to resolve that dilemma.

“That’s something we’ll have to work out,” Bacon said. “I’m not on the foreign — I’m not an ambassador, so I have no idea how they’re going to respond. Our guys want something that makes a difference on the border.”

Fitzpatrick said they’re “still ironing out the language” on the immigration side of the bill and added that it’ll be the Biden administration’s job to find a way to make Mexico comply.

“Well, that’s going to be part of what the administration’s role is in this,” he said. “We’re the legislative branch. The executive branch has to enforce the law.”

Fitzpatrick said he doesn’t have a commitment from Johnson to bring the bill to the floor. He said he’d do “whatever it takes” to advance the bill but downplayed the idea of a using a discharge petition — a tool to bypass leadership and force a vote — instead suggesting a “queen of the hill” rule in which many bills can get votes and the one with the largest number of votes is adopted.

“We have to talk to leadership or both parties, and hopefully they’ll support it,” he said, adding that he doesn’t have a firm timeline.

But Rep. Marjorie Taylor Greene, R-Ga., who has threatened to force a vote to overthrow Johnson if he puts a Ukraine funding bill on the floor, said the moderates’ bill is all but dead.

“I’ll assure you: Ukraine aid is not coming to the floor,” she said Thursday in an interview.

Unlike the Senate package, which passed 70-29, the House bill doesn’t include any humanitarian aid for those affected by war in Gaza, Ukraine and other hot spots; the aid would be solely for military needs.

But Fitzpatrick said lawmakers are free to try to change the legislation through the amendment process.

“We can open up to amendments and everybody can get their votes and let the House do its will,” he said.