As President Obama’s top aides watched the second debate on television backstage, there were multiple moments of outright jubilation. It was as if their sighs of relief in Hempstead, N.Y. could be heard in the Hamptons.

"Folks were just ecstatic,” said one person familiar with the scene. Even before they plotted the talking points for their post-debate media spin, they knew they had a far easier product to sell than they did after what they deemed the debacle of the first confrontation with Mitt Romney. They would not have to strain, as they did in Denver, to make lemonade out of lemons.

If they had privately graded him a “C” the first time, they were inclined to pass out at least an “A-minus,” if not higher, largely as a result of a performance they attributed in large measure to the disciplined handiwork of their boss, according to two sources familiar with the group’s private responses.

That pre-debate labor by Obama apparently included ample dissection of the tape of the first debate, as well as scrutiny of what Vice President Joe Biden did right in his face-off last week with Paul Ryan, these sources said.

In apparently important ways, the Biden performance, even with its seemingly theatrical excesses, was a benchmark. The president conceded that Biden had defended administration policy in a far more passionate and direct manner than he himself displayed in the previous encounter with Romney.

Obama can exhibit strains of personal diffidence, even condescension, toward people, especially critics. But aides portrayed his preparations for Tuesday’s showdown as a window onto a highly competitive politician who admitted his oratorical miscues and was intent on not repeating them. In the minds of aides, he also simply displayed more backbone Tuesday against a rival who proved a bit flustered and not nearly as effective as previously.

“He was on his game,” said one of his loyalists, “while Romney just wasn’t really on his.”

They were especially buoyed by the debate’s finale, amid what was deemed a stumbling by Romney over the administration’s response to the murder of the U.S. ambassador in Libya and a pointed and strong closing in which Obama drew clear lines of policy distinction.

Still, at least two sources also conceded that, by the light of day, there would be the overarching reality: the race remains close, with Romney having clearly cut into the president’s lead.

They hope they will get a significant “bounce” from his performance—albeit a modest one. Still, they’ll count it as a victory, given what had been the amount of momentum Romney generated in their first face-off.

“There was real damage done in Denver,” said one aide. “Tonight, he shored himself up.”