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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 CantorEric Cantor offering advice to end ‘immigration wars’ Trump's olive branch differs from the golden eras of bipartisanship After divisive rally, Trump calls for unity MORE (R-Va.) and House Judiciary Committee Chairman Bob GoodlatteBob GoodlatteOvernight Cybersecurity: Equifax security employee left after breach | Lawmakers float bill to reform warrantless surveillance | Intel leaders keeping collusion probe open House bill set to reignite debate on warrantless surveillance Warrantless wiretapping reform legislation circulates on Capitol Hill 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.