Originally Published: 23 JAN 24 16:34 ET

Updated: 24 JAN 24 17:06 ET

By Lauren Fox, Manu Raju, Ted Barrett and Melanie Zanona, CNN

(CNN) -- Republicans engaged in a tense back-and-forth during their conference lunch Tuesday over border talks with some openly questioning Senate Minority Leader Mitch McConnell’s strategy and others assailing colleagues for attacking the proposal before it’s even out.

“I think everyone is questioning everyone’s strategy on this,” said Sen. Joni Ernst, an Iowa Republican. “What’s the best way forward? I think that’s what people want to know and understand.”

The fight illustrates the increasingly perilous path ahead to pass any proposal on immigration – tied with aid to Ukraine and Israel – as Republicans remain divided over whether to cut a deal with Democrats on the high-profile issue in the middle of a presidential election.

During the meeting, Sen. Ron Johnson of Wisconsin questioned McConnell’s leadership on the issue, two sources told CNN, just a day after saying publicly that the Kentucky Republican couldn’t negotiate his way out of paper bag.

“It was a good debate. This is tough policy,” Sen. John Hoeven, a North Dakota Republican, said. “Some of it was boisterous.”

One Republican in the meeting said lunch was “nasty, nasty.”

“It’s an ugly place in the conference right now,” the member said on the condition of background to speak freely about what had occurred. “People are attacking Mitch openly in a way I haven’t seen … to his face.”

The moment comes as McConnell has told his conference that this moment may be the best one Republicans have to address border security and as he finds himself as a leading advocate for Ukraine aid when support for that in his party has started to crater.

The tension also comes as there is growing concern among some Senate Republicans that they could walk the plank on a border bill that seems to be going nowhere in the House and as the leading contender for the GOP presidential nomination Donald Trump is signaling he thinks Republicans shouldn’t back any deal unless it is exactly what the party wants.

“People are shadow boxing right now and that is because people don’t have specific text and (chief Republican neogtiator) James Lankford is doing everything he can to address the legitimate concerns,” said Republican Sen. Thom Tillis of North Carolina.

One source said Tillis was animated in a back-and-forth with Sen. Ted Cruz of Texas, something Tillis argued was just a typical exchange, adding, “It was a noisy group. I felt like I should use the voice that I developed with having five brothers and sisters.”

Another source in the room described the lunch as something akin to “the House of Commons.”

During the meeting, Johnson also handed members a graph he made showing various policies since 2012 and the impact they had on border encounters. He projected the graph into future years if a border deal – as he understands it – was enacted with border flows hovering at a high level even if they were down from where they had been the last several years.

“I’m still looking for an answer in terms of how do we prevent this,” Johnson told reporters pointing to his chart after the meeting. “I still don’t have it. I don’t know how we prevent normalizing 4- to 5,000 people a day coming across our border.”

“I think people have strong feelings,” Sen. Shelley Moore Capito of West Virginia said of the lunch. “But it it’s good to air it all out and hear the differing opinions whether it’s policy, politics or whatever. I didn’t get the sense that anybody was overly ticked off at any one specific person.”

Pressed on if McConnell caught some heat, Capito said it’s not unusual for people to take shots at the leadership.

“There are shots at the leadership, but there are also shots at others,” Capito said. “We are grownups. We can handle it.”