"The Senate proposal would dramatically increase illegal immigration."

A bipartisan group of senators is expected on Tuesday to unveil a plan to put millions of people living in the U.S. illegally on a path to legal residency. But Republicans like Smith continue to argue that doing this before fully controlling the U.S. border will only invite more people to enter illegally.

Smith said the Government Accountability Office has found that only 6 percent of the U.S.-Mexico border is secure, and that 40 percent of people now in the country have overstayed their visa. He said the Senate's bill fails to address the visa issue.

"The Senate proposal legalizes almost everyone in the country before a system is set up to identify the visa over-stayers," he said. "The Senate proposal amounts to amnesty first, border security later, if ever. It is fatally flawed."