The Obama campaign is doubling down on the argument that Mitt Romney's budget plan doesn't add up (or, as former President Bill Clinton tells it, doesn't pass the "arithmetic test"), meaning higher taxes on middle class and/or exploding deficits.

A new 30-second TV spot titled "Won't Say" begins airing today in Iowa, Nevada, Virginia and Ohio, the campaign said, hammering the Republican presidential nominee for personal secrecy with his own taxes and the specifics of his proposed tax reform plan.

"You could lose the deduction for your home mortgage, college tuition, health care," the narrator says. "How much would you pay? Romney just won't say."

You can watch the spot HERE.

Democrats have for weeks been prosecuting Romney's plan to cut tax rates by $5 trillion for wealthier Americans while pledging not to grow the deficit or impact middle-income earners. Their charge was emboldened on Sunday after Romney and running mate Rep. Paul Ryan struggled to explain how they would offset the cost when asked about for specifics on the Sunday talk shows.

"Romney's tax and budget plans are a riddle wrapped inside a mystery wrapped inside a total sham," writes Obama campaign policy director James Kvaal in a memo to be released Wednesday.

"Governor Romney and his advisers frankly admit that they won't reveal their policy plans because it would make them less likely to be elected," he says. "There is no way to pay for Romney's tax plan without raising taxes on middle class families, and there is no realistic way for Romney to address our unsustainable budget deficits, even if he guts the investments we need in the future of the middle class."

Because of the ambiguity, independent analysts like the nonpartisan Tax Policy Center, whose work the Romney campaign disputes, have had to deploy a host of assumptions in rating the Romney plan, ultimately concluding that taxes would effectively rise on middle class families.

Romney insists that his plan would not increase the tax burden on middle-income families. But in an interview Sunday on "Meet the Press," he could not provide an example of a tax loophole that he would close to help pay for a new round of tax cuts.

"I can tell you that people at the high end, high income taxpayers, are going to have fewer deductions and exemptions. Those numbers are going to come down. Otherwise, they'd get a tax break," Romney said.

"And I want to make sure people understand, despite what the Democrats said at their convention. I am not reducing taxes on high income taxpayers. I'm bringing down the rate of taxation, but also bringing down deductions and exemptions at the high end so the revenues stay the same, the taxes people pay stay the same. Middle income people are going to get a break. But at the high end, the tax coming in stays the same. But we encourage small business, because small business is able to keep more of what it makes and therefore hire more people, which is my priority."

UPDATE: In a statement, Romney campaign spokeswoman Amanda Henneberg called the ad a "misleading attack" meant to distract from Obama's plan to "raise taxes on small businesses and job creators" by letting the Bush-era tax breaks expire on families earning more than $250,000.

"Mitt Romney has a plan to lower rates across the board, spur investment, and finally get the country back on the right track," she said.