Graham and McCain optimistic after White House immigration meeting

(CNN) – Two leading Republican senators voiced optimism Tuesday after a sit-down with President Barack Obama focused primarily on the hot button topic of immigration.

Republican Sens. Lindsey Graham and John McCain both said the meeting at the White House went well, though didn't delve into what specifically was discussed. Graham, who has opposed Obama on topics ranging from national security to budgets, said it was "one of the best meetings I've ever had with the president."

"I was quite frankly encouraged," Graham told CNN. "I think we'll have presidential leadership in a very productive way on immigration reform."

"I think the president's very sincere in wanting a bill and wants to know what he can do to help," Graham, who represents South Carolina, continued. "I told him the talks were going good, me and Sen. McCain are working well with our colleagues."

McCain, on his way to cast a "no" vote for Obama's nominee to become defense secretary, said the immigration meeting was "excellent."

Asked what else what discussed, the Arizona lawmaker said "a number of issues but immigration was the major topic."

An early backer of comprehensive immigration reform, McCain later backed away from supporting a path to citizenship for undocumented immigrants after his position hurt him with GOP primary voters during his run for president in 2008. This year, he's been more vocal in his support of immigration reform measures, including a bipartisan framework proposed last month in the Senate.

That plan includes a pathway to citizenship that hinges on bolstering border security. Asked Tuesday whether he thought the president would sign a bill making border security a condition of a pathway to citizenship, McCain said "You'll have to ask him, but he understands the parameters of what we're doing."

Graham also said he thought Obama "understands that we need border security that we can afford."

In an interview Sunday, McCain explained improving border security and creating a pathway to citizenship were necessary and supported by the American people.

"Just because they broke the law doesn't mean they're condemned forever to a twilight status," he said on CNN's "State of the Union."

"I believe that most Americans feel that for these people who have come illegally, as long as they pay back taxes, pay a fine, learn English and get behind everybody else, that's a key element of it. And most Americans now realize we can't have 11 million people sit in the twilight, the shadows of America, forever."

McCain later said that Republicans won't be punished by conservative primary voters if they back comprehensive immigration reform legislation.