"It's one of the best meetings I've ever had with the president," Graham, R-S.C., told reporters. "Senator McCain made a strong point about the border, and the president understands the working components of it, so I was quite frankly encouraged.
"I think we'll have presidential leadership in a very productive way on immigration reform, and with that, we've got a very good chance of doing it this year."
Graham and McCain, R-Ariz., declined to give details of their discussion with Obama and Vice President Joe Biden, Roll Call reported.
But Graham said the Democratic president "committed himself and his office to be helpful, and I believe him."
"He wants to be a helpful entity here. ... I couldn't have been more pleased," Graham said.
McCain said Obama "understands the parameters of what we're dealing with." The Arizona senator wouldn't say whether an agreement the issue of border enforcement being linked to a pathway to citizenship.
"I believe that the president is very committed to comprehensive immigration reform," McCain said. "Now, does that mean he's committed to anything we do? No, he has his positions on the issue as well."
Notable deaths of 2014 [PHOTOS]