President Obama’s deputy campaign manager admitted yesterday that Obama’s claim that Mitt Romney wants to cut taxes by $5 trillion is false.

Stephanie Cutter initially stood by Obama’s claims during an interview with CNN’s Erin Burnett. “It’s a $5 trillion tab,” she said of Romney’s tax cut proposal.

“But then when you close deductions it’s not going to be anywhere near $5 trillion,” Burnett countered. “That’s our analysis.”

Cutter admitted she was right. “Okay, stipulated, it won’t be near $5 trillion,” she conceded. “But it’s also not going to be the sum of $5 trillion in the loopholes he’s going to close.”

Obama clearly thought the $5 trillion talking point was important during the debate. “Governor Romney’s central economic plan calls for a $5 trillion tax cut on top of the extension of the Bush tax cuts,” he said Wednesday. “How we pay for that, reduce the deficit, and make the investments that we need to make without dumping those costs onto middle-class Americans I think is one of the central questions of this campaign.”

He reiterated that argument in a post-debate rally yesterday morning. “Governor Romney cannot pay for his $5 trillion tax plan without blowing up the deficit or sticking it to the middle class,” Obama said in Denver.

Romney contradicted that point during the debate. “First of all, I don’t have a $5 trillion tax cut.  I don’t have a tax cut of the scale that you’re talking about.  My view is that we ought to provide tax relief to people in the middle class.  But I’m not going to reduce the share of taxes paid by high-income people.

The Romney campaign jumped on Cutter’s remarks on CNN. “Independent fact checkers – and even his own campaign – have admitted that President Obama is spreading falsehoods about Mitt Romney’s tax plan,” spokeswoman Amanda Henneberg said in a statement. “It’s clear the President is willing to say and do anything to avoid talking about his own record of fewer jobs, declining incomes and record poverty.”