President Barack Obama, escorted by House Sergeant at Arms Paul Irving, right, arrives on Capitol Hill in Washington, March 13, 2013, for closed-door talks with House Speaker John Boehner and the House Republican Conference to discuss the budget. (J. Scott Applewhite/AP Photo)

President Barack Obama said his meeting today with House Republicans was "useful," closely matching the assessment of House Speaker John Boehner, who called the meeting "productive."

"It was good, I enjoyed it," Obama said of the closed-door meeting, which ran 30 minutes longer than planned. "It was useful."

"We had a very frank and candid exchange of ideas and, frankly, I think it was productive," said Boehner, R-Ohio. "However … there are some very real differences between our two parties."

Despite the continuing standoff, Boehner said the tone of the meeting from the president and Republicans "was very respectful."

"I heard what the president had to say. I've heard it before. I thought it was good for all of our members to hear it so they have an understanding of where he's coming from," Boehner said. "We got big problems in our country. They need to be addressed. We're willing to get them addressed. I hope the president continues his outreach."

The president emerged from the meeting after about 90 minutes, disclosing that during the meeting he told lawmakers that the College of Cardinals had chosen a new pope. The white smoke and bells did not begin to signal the new pope until the president's meeting at the Capitol was already underway.

"I made the announcement that we saw smoke, but I actually have not seen the official announcement in name so we look forward to hearing about it - and I'm sure it's going to be big news," Obama told reporters after the meeting.

Asked whether there was a hint of white smoke at the Capitol, the president responded, "You're straining the analogy."

While no deal was reached to address the country's growing debt, the speaker said the meeting was "a good start" and expressed hope that conversations with the president continue.

"Republicans want to balance the budget. The president doesn't," Boehner said. "Republicans want to solve our long-term debt problem. The president doesn't. We want to unlock our energy resources to put more Americans back to work. The president doesn't.

"Even though we have very real differences," he added, "our job is to find common ground, to do the work the American people sent us here to do."