An effort to pass immigration legislation in piecemeal fashion is moving forward in the House, where most Republicans are supportive of measures to tighten border security and address millions of illegal immigrants already in the country, Rep. Trey GowdyHarold (Trey) Watson GowdyWhite House lawyer’s presence at FBI meetings sets off alarm bells for Dems Dems after briefing: 'No evidence' spy placed in Trump campaign House GOP sets three FBI interviews in Clinton probe MORE (R-S.C.) said.

Gowdy, chairman of the House Judiciary Subcommittee on Immigration and Border Security, noted in a Bloomberg interview with Al Hunt that the panel had already approved bills to strengthen the nation’s electronic worker verification system and overhaul guest worker and visa programs.

“So I don't think we're going to have a comprehensive bill where everything is put together, but some of the pieces fit naturally together," Gowdy said.

The strategy stands in contrast to that of the Senate, which passed a single seeping bill two weeks ago and is waiting for the House to act.

Gowdy said the House bills would likely not get a vote on the floor until after the August recess, and acknowledged that there are as many as 20 Republicans in the chamber that would just as soon scrap the entire effort until the next Congress.

“I also think that we should be prepared to walk away at some point if our principles are not being honored and not being followed,” Gowdy said. “But I don't think you go into it assuming that a worst-case scenario, therefore, I'm not going to even go to the dance.”

Gowdy estimated that 85 percent of the conference is supportive of passing some legislation. But he downplayed the political risk to the Republican Party if Congress doesn’t pass a comprehensive bill, noting that former President George H.W. Bush got a smaller portion of the Hispanic vote than his predecessor, President Ronald Reagan, after the 1986 amnesty of illegal immigrants.

“So I don't think we are one amnesty bill away from electoral success with Latino and Asian voters,” he said.

Gowdy said he doubted any immigration reform bill would be signed by December, but said he said the House could be in the final stages of negotiation by then.

“And I would not be surprised if we were not on the precipice of a conference or at least debating the principles of a conference committee,” he said.