The three Republican congressmen saw it as a rare ray of sunshine in Washington’s stormy budget battle: an invitation from the White House to hear President Obama lay out his ideas for taming the national debt.

They expected a peace offering, a gesture of goodwill aimed at smoothing a path toward compromise. But soon after taking their seats at George Washington University on Wednesday, they found themselves under fire for plotting “a fundamentally different America” from the one most Americans know and love.

“What came to my mind was: Why did he invite us?” Rep. Dave Camp (R-Mich.) said in an interview Thursday. “It’s just a wasted opportunity.”

The situation was all the more perplexing because Obama has to work with these guys: Camp is chairman of the House Ways and Means Committee, responsible for trade, taxes and urgent legislation to raise the legal limit on government borrowing. Rep. Jeb Hensarling (Tex.) chairs the House Republican Conference. And Rep. Paul Ryan (R-Wis.) is House Budget Committee chairman and the author of the spending blueprint Obama lacerated as “deeply pessimistic” during his 44-minute address.

At a time when the parties risk economic catastrophe unless they can come together to raise the debt limit, Obama’s partisan tone made no sense, Republicans across Capitol Hill said Thursday. Even some Obama allies wondered whether the president had made a tactical error.

“Yes,” the tenor of the speech was surprising, said Erskine Bowles, who headed Obama’s fiscal commission and is working with a bipartisan group of six senators to develop a compromise plan to rein in borrowing.

Asked about the president’s decision to deliver such an address at a particularly sensitive moment, Bowles defended Obama, and said his sharp tone would not derail the bipartisan group’s work. “This is not easy,” he said. “There are plenty of opportunities to make mistakes.”

At two Chicago fundraisers for his reelection campaign Thursday night, Obama defended his GWU speech. “That wasn’t a critique,” he said of his repeated attacks on Ryan’s ideas. “That was a description.”

“What we now have is a very stark choice,” Obama told a group of about 50 donors at a Chicago restaurant called MK. “Under their vision, we can’t invest in roads and bridges and broadband and high-speed rail. I mean, we would be a nation of potholes, and our airports would be worse than places that we thought -- that we used to call-- the Third World, but who are now investing in infrastructure.”

At an another appearance, Obama said: “The speech I gave yesterday [Wednesday] was not a partisan shot at the other side. It was an attempt to clarify the choice that we have as a country right now.”

The president argues the GOP budget will drastically will reduce infrastructure spending. But he offered no specific evidence the Republican spending reductions would actually affect American airports.

Administration officials note that Ryan and other Republicans have been just as pointed in their attacks on Obama.

“What the president did yesterday was describe the vision put forward by the House Republican plan and describe his own vision, the vision that he thinks is preferable,” Carney said Thursday. “Just because there’s a lot of heat in these discussions, in these debates, a lot of firmly held convictions, doesn’t mean that we cannot come together and find common ground.”

Still, Republicans said, did Obama have to attack the men to their faces? “Reagan had the decency to insult his enemies when he was out of town,” grumbled one GOP aide.

For Ryan, the misadventure began Sunday morning, when he was bumped from the lead spot on “Meet the Press” by David Plouffe, the senior White House political adviser, who suddenly appeared on the show to discuss the president’s new deficit-reduction plan.

In retrospect, Ryan said, Plouffe’s presence should have been a red flag.

“I’m, like, well, if it’s a deficit plan, and they’re serious about it, why isn’t [White House budget director] Jack Lew or [Treasury Secretary] Tim Geithner rolling it out?”

Still, when Ryan, Camp and Hensarling were invited to attend the speech because they had served on Obama’s fiscal commission, Ryan concluded that Obama was extending an “olive branch” in the budget wars and that it would be good form to attend.

Afterward, Ryan was furious. The speech “was extremely political, very partisan,” he fumed to TV host Charlie Rose.

Camp said he received a call from fiscal commission co-chairman Alan Simpson, who was also in the audience and was “concerned about the partisan nature of the event and how unnecessary and unproductive and unhelpful it would be.”

By Thursday afternoon, Camp, who works regularly with Geithner and other senior administration officials, was still pondering whether to call someone at the White House.

“But then I thought, maybe if I can’t figure out who to call, they need to call me,” he said. “It’s their agenda they need to get through the House.”

Staff writer Perry Bacon Jr. contributed to this report.