Many Republicans are worried that even passage of a House border security bill might lead to a House-Senate conference that produces a bill that includes language creating a path to citizenship for illegal residents. For that reason, the resolution states that no bill, "including any conference report regarding immigration," should be considered on the House floor until the southern border is secure.

The resolution finds that existing immigration laws need to be enforced "vigorously and uniformly," and that the government failed to adequately enforce the border provisions in the 1986 immigration law.

"[A]ccording to a 2010 Rasmussen poll 68 percent of likely voters think that securing the border is more important than granting amnesty to illegal aliens," it reads. It also notes that President Obama "previously promised to secure the U.S. border with Mexico," but has enacted policies that "deliberately undermine immigration enforcement laws."

The House left for the August break without passing any immigration legislation. But GOP leaders have said they would try to pass something in the fall, which could be language on tighter border enforcement or increased visas for skilled workers.

It's not clear, however, whether these proposals can pass given Democratic demands for language allowing a path to citizenship, and Republican fears that passing any bill would help advance the Senate bill.