Republican congressman Bob Goodlatte of Virginia also said at a town hall meeting in the Shenandoah Valley that he'll do everything he can to ensure the House never takes up the Senate's comprehensive immigration bill, which includes a path to citizenship for the 11 million immigrants in the country illegally.

Goodlatte said the House will proceed with individual immigration bills once lawmakers return to Washington in September from their summer recess, beginning with bills on interior enforcement, border security and workplace verification.

The focus of the House's Republican majority should be on how to "reform immigration the right way to show how it should be done, even if it doesn't go all the way through to be signed by this president. Because I have a hard time, like you do, envisioning him signing some of these things," Goodlatte told one questioner. "It doesn't mean we shouldn't at least show the American people that we are interested in solving this very serious problem that we have in our country."