(CBS News) President Barack Obama has claimed that Mitt Romney's tax numbers do not add up, arguing that the Republican presidential candidate's promise to lower tax rates for all families can't be paid for without cutting popular tax deductions for middle class families.
Vice President Joe Biden repeated the claim during last week's vice presidential debate, saying, "The only way you can find $5 trillion in loopholes is cut the mortgage deduction for middle class people."
Mitt Romney has argued lower rates will stimulate the economy, and he is emphatic the middle class won't pay.
"I will not under any circumstances raise taxes on middle-income families," he said during the first presidential debate on Oct. 3.
Romney's plan starts by lowering tax rates 20 percent for everyone. It's a major tax cut that the non-partisan Tax Policy Center said will cost the federal budget $480 billion a year, or roughly $5 trillion over 10 years.
But Romney and running mate Paul Ryan say they will offset those costs by reducing tax deductions. They won't specify which ones, saying that would be worked out with Congress. But they promise they will only target the rich.
In theory, there is plenty of money to be found in tax deductions -- $1.1 trillion a year -- but the most valuable deductions don't just benefit the rich.
The tax-free benefit workers receive when employers pay for health insurance, the tax deduction for mortgage interest and the tax-free contributions workers make to 401(k) pensions are all heavily used by both rich and middle class and are all politically popular.
Maya MacGuineas, president of the non-partisan Committee for a Responsible Federal Budget, said that until Romney releases more details, it's not clear if he can pay for the tax cut.
"The question is, can you do it without going into the middle class at all," MacGuineas said. "That's the big question that the governor has claimed, but we haven't seen the numbers either way to know whether for sure it's doable."
Romney's argument that it is possible to avoid raising taxes on middle class families depends on two assumptions. One is that lower tax rates will lead to jobs, to more people paying taxes and then to a lower deficit. The other assumption is that a deal to cut into the popular tax deductions can be reached with a divided Congress.