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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 Ivan CantorThe Hill's Morning Report — Sponsored by CVS Health — Trump’s love-hate relationship with the Senate Race for Republican Speaker rare chance to unify party for election Scalise allies upset over Ryan blindside on McCarthy endorsement MORE (R-Va.) and House Judiciary Committee Chairman Bob GoodlatteRobert (Bob) William GoodlatteConservatives express concern over House GOP immigration bill Republicans tear into IG finding on Clinton probe Trump vows to stand with House GOP '1,000 percent' on immigration 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.