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 Gowdy (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.