“Respecting the conversations and negotiations that are going on among the seven of us – and I want to respect a good friend, Mario Diaz-Balart, and what he says – but he's absolutely wrong,” Becerra, who heads the Democratic Caucus, said Tuesday during a press briefing in the Capitol. “Let me repeat that: What he has said is absolutely wrong.”

Rep. Joseph Crowley (D-N.Y.), the vice chairman of the Caucus, piled on.

“Not being a member of the [group], let me just say that what Mario Diaz-Balart has said is absolutely wrong,” Crowley said.

The comments arrive as the House negotiators are struggling to finalize a comprehensive immigration reform bill as an alternative to the bipartisan Senate package that's on the floor of the upper chamber this month.

Becerra last week had predicted the group would release an agreement soon, but the California liberal backed away from that forecast Tuesday.

“This bipartisan group is intent on producing a bill, but I'm going to stop making predictions,” he said.

Complicating the House talks, Rep. Raúl Labrador (R-Idaho), one of the GOP negotiators, abandoned the group this month, citing his opposition to taxpayer-subsidized healthcare benefits for immigrants living in the U.S. illegally.

Diaz-Balart on Monday said the healthcare issue continues to be the final significant sticking point, and he accused Pelosi and Democratic leaders of scuttling a pair of agreements initially supported by the group's Democratic negotiators.

“I think the problem that we're running into is Nancy Pelosi,” Diaz-Balart told MSNBC. “I'm not quite sure if she wants a bill.”

Pelosi all along has insisted she wants a deal, vowing that Democrats are ready to make sacrifices in order to pass comprehensive reforms this year.

“Anybody who would say that I would rather have the issue than the bill just doesn’t know what they’re talking about,” Pelosi told reporters Thursday in the Capitol.

Becerra on Tuesday left no questions about whose side he's on.

“What Mario Diaz-Balart said is totally untrue,” Becerra said. “This stuff about pointing fingers has to stop. We've just got to get the work done.”

Speaker John BoehnerJohn BoehnerLobbyists bounce back under Trump Business groups silent on Trump's Ex-Im nominee Chaffetz won't run for reelection MORE (R-Ohio) churned headlines Tuesday morning when he vowed not to stage a vote on any immigration reform bills that fail to win the support of a majority of his Republican conference.

“I don't see any way of bringing an immigration bill to the floor that doesn't have a majority support of Republicans,” BoehnerJohn BoehnerLobbyists bounce back under Trump Business groups silent on Trump's Ex-Im nominee Chaffetz won't run for reelection MORE told reporters in the Capitol.

That decision is likely to disappoint Democrats and some Republicans who see conservatives in the House as the largest hurdle to securing a comprehensive reform deal this year.

Indeed, Diaz-Balart on Monday said fixing the immigration system with bipartisan support is more important than how the bill ultimately passes.

“The right move is to make sure that we have bipartisan support, frankly. I'm less concerned about, you know, if it's, you know, how many Republicans, how many Democrats,” he said. “I think we to have buy-in from both.”

The Congressional Hispanic Caucus will also meet privately with Boehner on Wednesday.

A leading Democratic advocate for immigration reform, Rep. Luis Gutiérrez (Ill.), however, said the group would not necessarily push the Speaker to bring up the issue if it lacks support from a majority of Republicans.

"I don't know that he can do it," Gutiérrez said on Tuesday. 

"Here’s what I believe he can do, and I hope he will embrace: a bipartisan route on comprehensive immigration reform," he said.

Gutiérrez, a member of the bipartisan House immigration group, nonetheless said he believed a majority of the House would back a comprehensive bill.

"I hope in the end that this doesn’t become a partisan issue and that they allow a majority of the House of Representatives, who really represent a majority of the people of the United States of America, to vote their will," he said. 

"I will bet every ounce of my reputation, my political reputation for being able to count votes, that the votes exist in the House of Representatives. The votes exist. There are more than [218] for comprehensive immigration reform,” Gutiérrez added.

Russell Berman contributed

This post was updated at 1:25 p.m.