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Cantor: 'Distrust' Of Obama Among GOP On Enforcing Laws, Immigration

AP Photo / J. Scott Applewhite

Cantor said that immigration will not be the main focus of the House Republican conference this legislative session, though.

"I believe that you're going to see us, in Congress, not only continue this discussion on immigration, but we want to try to get to the heart of the issues that are affecting most Americans," he said.

When asked by host Major Garrett whether the House GOP will consider legal status or a path to citizenship for undocumented immigrants, Cantor talked about Republican willingness to provide young undocumented immigrants with legal status.

"We've said all along we don't believe in a comprehensive fix. We want to go in a step-by-step approach to try and address the problems," he said. "I've always said we ought to be dealing with the things that we can agree on, which are the kids."