"I'm just going to move on and work with other members of the House Judiciary Committee to try to craft legislation that can actually ... pass the House," the Idaho Republican told reporters Wednesday night after an hourlong meeting other Republicans described as leading almost to a tentative bipartisan agreement on a comprehensive deal to overhaul U.S. immigration laws.
"We just couldn't agree on the healthcare language, and I think we've been going around in circles on the healthcare language for a long time," said Labrador, the most recent addition to the so-called House Gang of Eight that had met in secret for four years.
He said he didn't want to hold up the group, but he also said he would now write an immigration-reform bill he feels comfortable with.
"There will be a Republican plan," he said. "Whether it is a bipartisan plan or just a separate partisan plan, there will be something that passes the House of Representatives."
Labrador is a conservative Latino Republican like Sen. Marco Rubio of Florida, who serves on the Senate's bipartisan Gang of Eight immigration-reform group. They both are widely seen as playing instrumental roles in selling a comprehensive immigration reform effort to their party.
Three Republicans remain in the House gang -- Mario Diaz-Balart of Florida, and John Carter and Sam Johnson of Texas.
Carter and Diaz-Balart said they considered the Wednesday night meeting a success, without mentioning Labrador's departure.
"We have found a way forward," Carter said.
"This is a very complicated, complex issue, but I'm very optimistic as to where we're headed," Diaz-Balart said. "I really am. I really, really am."
Labrador said: "If they want to agree with the Democrats on something, I don't think I should stand in their way. But I just can't agree with them."
Rep. Luis Gutierrez, D-Ill., another member of the House gang, told reporters he hoped the group would "make an announcement pretty soon."
About "80 percent" of the bill has already been drafted and negotiators agreed on about "95 percent" of the immigration package, he said.
Celebrity Families of 2014 [PHOTOS]