In his first meeting with House Republicans in two years, President Obama strongly pushed back on the charge that his administration’s top priority is to score political points against the GOP.

“This thing that everything we do is designed to gain a political advantage on you is just not true,” Obama said during a tense but respectful 80-minute meeting Wednesday afternoon in the Capitol basement, according to a source in attendance.

“I got 75 percent of the Hispanic vote. I got 75 percent of the Asian vote. If you tank immigration reform, it would be great for Democrats,” the president continued, offering an example of a policy prescription that wouldn’t necessarily pay dividends for his party.

Republican lawmakers say many of the questions posed to the president during the rare face-to-face session conveyed the implicit trust deficit between their caucus and the White House.

The appearance came in the midst of stalled debt-reduction negotiations and just a day after Rep. Paul Ryan unveiled a House GOP budget that was roundly attacked by Democrats.

Yet Obama is keenly aware that if he is to cement his legacy with a comprehensive immigration-reform package and a grand bargain to slash the deficit, he’ll need to chip away at the ice that has largely frozen his relationship with House Republicans.

In part, he attempted to do thaw relations by reverting to a favorite theme: a lament of the media culture.

“When we get our news in this town, it’s a closed loop. The GOP has Fox News; Democrats have MSNBC on their TVs. You should read The Huffington Post and see how I’m getting slapped around by the left. They think I’m giving everything away to you guys every day,” Obama implored at one point during a lengthy answer, according to two lawmakers.

By and large, rank-and-file GOP members expressed appreciation for the president’s effort, but said they weren’t convinced that he wouldn’t try to ramrod them once the rubber met the road on policy.

“The president defended himself to the extent that he could with all of us recognizing that he’s meeting with [Organizing for Action] tonight. His defense of that was, ‘Oh, it’s a policy group and not a political group.’ Well, so is the Saturday Republican lunch club,” swiped Colorado Rep. Cory Gardner. “I think it’s disingenuous to think that they’re going to be pushing policy and leaving politics at the front door.”

The second-term congressman said he was disappointed the president didn’t voice more willingness to give ground on issues like entitlement reform.

According to attendees, Obama acknowledged that he would consider significant changes such as indexing Medicare benefits, but noted, “I can’t do everything this conference wants and nothing the other side wants.”

“He seems to be more of the mind of sort of extracting a pound of flesh,” Gardner said when asked about the president’s tone on making changes to safety-net programs.

Freshman North Dakota Rep. Kevin Cramer said he was struck by just how much the cable-news kibitzers and partisan commentators appeared to weigh on Obama’s mind.

“I find him to be quite interested in politics. You don’t usually expect the president to use such specific, partisan political imagery,” Cramer said, referring to the president’s comments on particular media outlets. “I was like, wow, really? I don’t even have time to watch Fox News ... I actually found him to be more of a political junkie than someone would expect someone at his level to be.”

Other topics at the meeting included gun control, tax reform, and the Keystone Pipeline, but most of the conversation centered around fiscal issues and whether the two sides could find daylight on an overarching budget deal.

According to Gardner, when Michigan Rep. Dave Camp asked Obama why the two sides couldn’t come together to act on the entitlement changes they agree on, the president reasserted that he wouldn’t budge without new taxes.

It’s the sticking point that has gummed up negotiations from the start—and little headway was made Wednesday.

“I think the skepticism on our side is, this guy really likes taxes,” said Louisiana Rep. Bill Cassidy afterward, adding that he would take a wait-and-see approach on Obama’s overture for bipartisanship. “Having seen him pillory the Romney-Ryan plan and get reelected on that kind of demagoguing of the issues, there’s some skepticism that he’s not setting us up to demagogue it again.”

Cramer said the ball was in the president’s court to seek common ground on the fiscal stalemate and zapped him for scheduling his budget delivery to Congress “in a couple weeks.”

“I wish his budget was as on time as he was,” he quipped.

Obama’s intransigence on extracting more revenue is likely explained by public opinion, which remains squarely in his corner in a bare-knuckled brawl with Congress.

While the latest Washington Post–ABC News poll pegs the president’s approval at 50 percent, an overwhelming 80 percent of Americans disapprove of Congress. The cherry on top for him: almost three quarters, 72 percent, disapprove of congressional Republicans.

That’s why this sustained charm offensive—Obama met with Senate Democrats on Tuesday and will meet with Senate Republicans on Thursday—can do no harm, even if it isn’t much help.

Besides, the session wasn’t completely a rigid exchange of ideological differences. An impromptu joke by Missouri Rep. Billy Long cut the tension for at least a few moments.

When an aide handed the president a note notifying him of white smoke at the Vatican, signaling the election of a new pope, Long asked, “Does that mean the White House is open for tours?”

“No,” the president replied with a grin over sustained laughter throughout the room, “but it means the Vatican is.”