That lawmaker and some of the others describing what occurred in the meetings spoke on condition of anonymity, noting that the sessions were supposed to be private discussions.
The politically fraught moment came at the outset of Obama's widely publicized recent string of meetings with rank-and-file lawmakers. The unusual commitment of presidential time netted public praise from his most implacable critics and was supplemented by numerous conversations among lawmakers and senior White House aides.
No breakthroughs were anticipated and none emerged, and for all the warm talk, House Speaker John Boehner delivered a tart summation.
"Republicans want to balance the budget. The president doesn't. Republicans want to solve our long-term debt problem. The president doesn't," he said, while adding it was incumbent on all sides to seek common ground.
Across the hours, there were moments of levity, and an expression of gratitude to Arizona Sen. John McCain for his service to the nation on the 40th anniversary of his release from a prisoner of war camp in Vietnam.
Evidently the food was pretty good, too.
One presidential aide left a meeting with the Senate Republican rank and file toting a carry-out bag from lunch that featured lobster salad and blueberry pie with ice cream.
"Ultimately it's a matter of the House and the Senate ... getting together and being willing to compromise," the president said as he departed the Capitol on Thursday.
Even on that point, Republicans disagree.
Over and over, they told Obama, he must lead, tone down the attacks on them and lean on Democrats to accept concessions in benefit programs.
Over and over, he told Republicans that if he is to make concessions on Medicare and elsewhere, they would have to agree to higher taxes.
On that, there was little if any give, particularly with Republicans noting that Obama's approval ratings have recently begun receding for the first time since his re-election.
At the dinner at the Jefferson Hotel more than 10 days ago, Republican senators noted that some of the changes under discussion for Medicare would raise costs for wealthier seniors and also that higher revenues might result from what one called "pro-growth tax reform."
But there was no support for raising taxes, recalled one participant at the dinner. Several said the resolve stemmed from last winter's agreement to raise tax rates in legislation that contained only skimpy spending cuts.
By the time of his final meeting Thursday, Obama told House Democrats that, for now at least, they needn't worry about having to make concessions like slowing the growth of cost-of-living benefits under Social Security and other programs. Republicans, he said, weren't willing to contemplate enough additional tax revenue to warrant the trade-off.
Policy differences aside, there was an undercurrent of mistrust if not long-nursed grievances among Republicans, many of whom were getting their first look up-close look at the Democrat in the White House.
Rep. James Lankford of Oklahoma told the president he had heard that his first call on election night last November had been to the leader of the Democrats' 2014 campaign committee, rather than to Boehner, the Republican speaker.
Not so, Obama replied, saying he had indeed called Boehner first, but he was asleep. "Yeah, it was an early night for us," called out one lawmaker, drawing laughs from a group that lost eight seats in November.
Later in the same meeting, Rep. Tom Price of Georgia referred to a lack of trust between the two sides. According to participants in the meeting, he chalked up Obama's delay in presenting a budget this spring to politics.
The president replied that if he were solely interested in politics he would be running a "Mediscare" campaign rather than holding meetings with Republicans.
Across the Capitol, Sen. John Thune of South Dakota singled out an interview in which he said the president accused Republicans of wanting to eviscerate Medicare, Medicaid and Social Security.
"Nobody here believes those programs ought to be gutted," Thune told Obama, the senator later recalled. Instead, he told the president that Republicans want to preserve the programs for the future.
The president stood his ground, saying the Republican plan to turn Medicaid and food stamps into all-purpose grants to the states would inevitably lead to deep cuts in services for the needy.
By all accounts, Medicare, which provides health care to millions of seniors, is the key to any deficit-reduction compromise.
In his budget a year ago, Obama proposed saving $305 billion over a decade from the program, although little of that derives from the sort of changes Republicans say are essential to slow the growth in health care costs.
Roughly half would come from drug companies that sell medicine to low-income Medicare beneficiaries. Also, $63 billion savings would come from changes in payment rules for post-hospital care facilities, and $36 billion from lowering the amount of bad debt the government would cover for providers.
An additional $28 billion would come from raising premiums for wealthier seniors beginning in 2017.
Rep. Dave Camp of Michigan, chairman of the House Ways and Means Committee, noted that the president had said repeatedly last winter that Congress should pass tax items they agreed on and leave others for later.
Seeking to turn the tables, he asked Obama why the White House wouldn't now agree to pass legislation to slow the growth of cost-of-living increases in Social Security and other benefit programs and increase Medicare fees for wealthier seniors. Those are steps Obama has backed in the past.
Obama replied that Republicans would have to agree to higher taxes first, according to several lawmakers present.
Even then, it was clear when he met with Senate Democrats that Obama would face resistance from his allies in Congress.
Sen. Bernie Sanders of Vermont, an independent who sides with Democrats, said he and Democratic Sen. Tom Harkin of Iowa spoke out strongly against changes in calculating cost-of-living increases.
"It would make major cuts in Social Security benefits ... and also very significant cuts for disabled veterans," Sanders said in a telephone interview.
"I do not believe that the American people want to balance the budget on the backs of disabled veterans or widows who lost their husbands in the wars in Iraq and Afghanistan."
Associated Press writers Donna Cassata and Charles Babington contributed to this report.