Republican Sens. Lindsey Graham and John McCain returned to the Capitol from their White House meeting with President Barack Obama and Vice President Joseph R. Biden Jr. more encouraged about the prospects for an immigration overhaul.

The duo declined to discuss the specifics of their conversation, but were broadly appreciative of the president for reaching out.

“It’s one of the best meetings I’ve ever had with the president,” Graham told reporters. “Sen. 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.”

The South Carolina lawmaker said the president showed he would be flexible.

“He committed himself and his office to be helpful, and I believe him.” Graham said. “He wants to be a helpful entity here. … I couldn’t have been more pleased.”

McCain declined to say whether Obama gave ground on the key question of whether a pathway to citizenship would be tied to border enforcement, but the Arizona Republican said the president “understands the parameters of what we’re dealing with.”

McCain said Obama wants a bill he can sign, not just a political issue.

“I believe that the president is very committed to comprehensive immigration reform. Now, does that mean he’s committed to anything we do? No, he has his positions on the issue as well.”

When asked whether Obama understands the border security issues McCain said, “I am more confident after our conversation today.”

McCain said that other issues were discussed as well but declined to give details.

Niels Lesniewski contributed to this report.