Rep. Cohen: Boehner will need Dem votes on immigration

"I don't know how they're going to come up with a majority of the majority and they're going to get a bill that they can pass and that would work with the Senate," Cohen said in an interview with C-SPAN. "I think they're going to have to have Democratic votes."

The focus on passing immigration reform has moved to the House after the Senate recently passed a bipartisan immigration reform proposal that offers a pathway to citizenship and also doubles fencing and border patrol agents along the U.S.-Mexico border. A number of House Republican lawmakers have argued that their chamber should ignore the Senate bill and seek to pass immigration reform as a set of smaller bills.

Cohen argued that it may also be difficult to rally a majority of House Republicans behind an immigration bill because some of them don't think it's necessary to reform the nation's immigration system.

"Some of the Republicans in the Tea Party don't think that's necessary," Cohen said. "They don't think that conventional wisdom is correct and they need to do that and some of them don't care because they're concerned, as most politicians are, about their own political stake and their own district. So it may be difficult for them to get a majority of the majority bill that can pass the Senate and the House both and become law."

House Majority Leader Eric Cantor (R-Va.) and House Judiciary Committee Chairman Bob Goodlatte (R-Va.) are drafting legislation that would offer citizenship to immigrant children who came to the country illegally through their parents. The bill, according to Cantor's office, is the "early stages" and will be the first proposal by House Republicans to reform a major part of the nation's immigration system.