President Obama reiterated his support for key changes to entitlement programs in a spirited exchange with House Republicans on Wednesday.

Emerging from the second day of meetings with lawmakers of both chambers and political parties, Obama deemed the exchange with his leading political nemeses "useful."

“It was good, I enjoyed it, it was useful," he told reporters as he left a basement conference room of the U.S. Capitol and headed back to the White House.

President Obama walks with House sergeant-at-arms Paul D. Irving (R) inside the U.S. Capitol to meet with House Republican Conference, on March 13, 013. (EPA/Molly Riley / POOL)

Lawmakers said the president's support for changing entitlements included possibly means-testing expensive retiree health programs and adjusting the way inflation is measured, which would have the result of reducing Social Security benefits over time.

In a key exchange, House Ways and Means Committee Chairman Dave Camp (R-Mich.) asked if Republicans could go ahead and move forward with entitlement changes with which Obama agrees, the president made clear he would take those moves only in exchange for additional tax revenues, according to Rep. Cory Gardner (R-Colo.).

"He asked 'Why let our differences get in the way of the things that we agree with?'" Gardner said. "The president insisted that -- this is how I would put it -- that he extract a pound of flesh from Republicans as well before he does that."

"I find that very frustrating," Gardner said. "There are $650 billion in tax increase already on the table, that the president already got. Why can’t we move forward on some of these meaningful reforms?"

Rep. Jeff Fortenberry (R-Neb.) said the two sides arrived at a familiar crossroads. "If we’re going to move forward on some reforms in the health care programs, it would have to be coupled with what he’s said all along -- additional tax revenues," he said. "So there’s an impasse there."

Some viewed the president's answers as a positive step, if nothing else because it showed effort at building a relationship that has so far only been forged in four meetings with the entire House GOP. "I think he did himself some favors," House Budget Committee Chairman Paul Ryan (R-Wis.) said.

But others exited the meeting saying that the two sides remained far apart on the key issues of how deeply to draw savings from entitlements and how high to raise new tax revenue. "Other than that, we're close," joked Rep. Darrell Issa (R-Calif.).

The president's attendance was part of a three-day charm offensive designed to jump-start talks with lawmakers at odds with his policies and openly frustrated by his lack of engagement with Congress.

The nearly 90-minute meeting opened with brief remarks by House Speaker John A. Boehner (R-Ohio) and Obama, but then was dominated by an hour-long question-and-answer session with GOP lawmakers, all rank-and-file members whose remarks ran the legislative gamut on key issues. Questions from lawmakers were pre-selected by Rep. Cathy McMorris Rogers (R-Wash.), the chairman of the GOP conference.

During the meeting Obama also broke the news of the selection of a new Roman Catholic Pope. Unaware that white smoke had begun billowing from the Sistine Chapel in Vatican City until an aide handed him a note, lawmakers said Obama announced that cardinals had selected a new pontiff, which prompted cheers.

"Does that mean the White House is open for tours?" asked Rep. Billy Long (R-Mo.), a question that lawmakers said prompted laughs from the crowd and the president.

Questions about the Keystone XL pipeline came from Republican Study Committee Chairman Steve Scalise (R-La.), who asked whether Obama will approve its construction.

"He talked about the upside of it. He talked about the downside of it. The over-hyped benefit versus the real benefit. He answered it carefully," Fortenberry recalled. "Clearly, he's deliberating still."

White House officials wouldn't comment on Obama's comments to Republicans.

On immigration, several Republicans said Obama made an unusual argument: It's in the GOP's own interest to cooperate on changes to immigration law. They said it was part of a broader case made by the president, insisting that he is working to advance the country as he sees appropriate, as opposed to working to defeat the Republican Party. Why would he encourage Republicans to participate in immigration changes if he only wanted to gain a political advantage, Obama reasoned.

"What I heard him say was that if he was truly interested in using immigration as a political wedge issue, then why would he be encouraging us to do something on it?" Gardner said.

Republicans broadly said they felt like Obama was respectful of their views and the conversation was substantive.

Asked whether he considered the meeting helpful, freshman Rep. Rodney Davis (R-Ill.) said, "I’m eight-weeks-old, so I don’t know. For me, it was the first time so I have to take it as a very positive step that the president is willing together with us and find some commonsense solutions.”

But Rep. Lee Terry (R-Neb.) suggested that he and other members weren't impressed by the president's new charm offensive.

"The spell didn't take, but it's one that needs persistency," Terry said -- smiling as he used a made up word.

"Let's just say I think there's built up over the past few years such an intense level of distrust that it will take more than just this meeting to repair it," Terry said.

The Omaha-area lawmaker noted that he was elected to Congress in 1999, in the final years of Bill Clinton's presidency.

"I had two years with President Clinton and had three different conversations with him," Terry said. "This one," he said, referring to Obama, "I've never had a hello back and forth from waving to him from 10 feet. I think that's really demonstrative of why there's so much distrust.

"I've written letters there and never even had replies. Nothing," Terry added. "No visit from their legislative staff. I don't even know the name of anybody in their legislative staff. So you hear the negative comments from the president about us, and you have zero contact with us, that's not a way you build trust. So maybe this is the day that changes all that."

Rosalind S. Helderman and Rachel Weiner contributed to this report.