The White House said that at the meeting, Obama "reiterated the key principles he believes must be a part of any bipartisan, commonsense effort, including continuing to strengthen border security" — a key sticking point in Senate negotiations.

The White House has objected to a Republican plan that would precondition a so-called pathway to citizenship for the nation's 11 million illegal immigrants on additional border security measures. Democrats have said that while they remain committed to improving border security, they fear leaving the process in limbo.

In his State of the Union address Tuesday night, Obama said "the time has come to pass comprehensive immigration reform."

"Real reform means establishing a responsible pathway to earned citizenship — a path that includes passing a background check, paying taxes and a meaningful penalty, learning English, and going to the back of the line behind the folks trying to come here legally," Obama said. "And real reform means fixing the legal immigration system to cut waiting periods, reduce bureaucracy, and attract the highly-skilled entrepreneurs and engineers that will help create jobs and grow our economy."

Following the address, Rep. Raúl Labrador (R-Idaho) — expected to be a shepherd of immigration legislation in the Republican House — told CBS News that he thought a deal could be done if Democrats were willing to concede some points.

"As long as the president and his party don't draw a red line and say that they have to get everything that they want," Labrador said.