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Sanford's comments, published on Tuesday, come as the spotlight moves to the House on passing immigration reform legislation. Top Republican lawmakers have said their chamber would not take up a bipartisan immigration reform proposal that passed the Senate in late June. Instead, the House is likely to pass a series of smaller immigration bills. 

"Again, what's probably going to happen is in the House side is there'll be a number of small micro bills that would be palatable to the body," Sanford told the Hilton Head Island Packet of South Carolina. Those bills include proposals on high skilled immigrants or a guest worker program for agriculture workers.

"And once one of those bills goes through, in essence, it becomes the train that takes it over to the conference —I mean over to the Senate, and you basically end up with a Senate bill," Sanford continued. "That's the concern of conservatives and that's probably what's going to happen."

A week earlier, House Majority Leader Eric CantorEric CantorTrump allies warn: No compromise on immigration Chamber of Commerce overhauls lobbying operation Laura Ingraham under consideration for White House press secretary MORE (R-Va.) and House Judiciary Committee Chairman Bob GoodlatteBob GoodlatteOvernight Tech: Last-ditch effort to get Dem FCC commish confirmed | Facebook's Sandberg on fake news | Microsoft completes LinkedIn deal House rejects GOP rep's push for vote on impeaching IRS head Overnight Regulation: Biz groups push reg reform in new Congress MORE (R-Va.) announced that they are drafting legislation that would offer a path to citizenship for children brought to the country illegally as children. That proposal would be the first Republican proposal out of the House aimed at addressing a major part of the nation's immigration system.