Durbin has consistently pushed support for his DREAM Act, which would allow younger, undocumented residents a chance at citizenship as long as they have graduated high school and spent two years in college or served in the military.

"The American people understand it makes no sense to deport these talented young people," he said. "They grew up in America, they can make us a better nation."

Immigration policy is expected to be a key issue in the next Congress, given that many Republicans believe they did not fare as well as they had hoped they would in last week's election because of their resistance to changes along the lines of what Durbin has proposed. Durbin said he sees signs that even Republicans are coming around, and asked Congress to pass a bill soon.

"I'm heartened and encouraged that so many are now speaking out in favorable terms of doing something," he said. "Let's get this done."