When Vice President Joe Biden debates Republican vice presidential nominee Paul Ryan tonight, you can be sure the $5 trillion question will come up.

In what has emerged as a major issue, the two presidential campaigns have engaged in a testy argument about Republican nominee Mitt Romney’s plan to slash income and investment taxes.

They don’t even agree on the size of the tax cuts being proposed, and certainly disagree over their potential impact.

To Romney, the tax cuts will ignite a spark in the sluggish economy. To President Barack Obama, they will blow a $5 trillion hole during the next decade into the federal deficit, forcing Romney either to slash federal spending or increase taxes on the middle class.

The fate of the election could rest on which argument carries the most swing voters.

“Either he raises taxes on middle class or he adds to the deficit,’’ said Michael Linden, a tax and budget analyst at the Democratic-leaning Center for American Progress in Washington. “It’s one or the other. He can’t have both. He has benefitted from the confusion he has created.’’

By contrast, Sen. Rob Portman, R-Ohio, said he has “been scratching my head over the $5 trillion number. There is no $5 trillion tax cut,’’ he said, insisting that the tax cuts Romney is proposing are closer to $4 trillion over the next decade and would be paid for by increasing economic growth and eliminating or capping deductions for the wealthy.

Here is what Romney has outlined: He wants to extend the 2001 and 2003 income and investment tax cuts for all Americans scheduled to expire at the end of the year. He also would push for an additional 20 percent income tax cut for all Americans, and repeal the estate tax and alternative minimum tax.

In return for lowering income tax rates, Romney pledges to either eliminate deductions and credits in the tax code or limit how much Americans could deduct from their taxes. He has argued the combination of lower tax rates and a more efficient tax code would lead to a more robust economy.

But Romney has yet to say which deductions he would eliminate, which has made his claims of the tax proposals being revenue-neutral difficult to substantiate.

Nobody doubts that the tax code is riddled with deductions and credits, some quite obscure. According to the congressional Joint Committee on Taxation, there is a deduction for fertilizer and soil conditioning costs, a credit for plug-in electric cars, a deduction for timber growing costs, and tax credits for solar, geothermal, and wind power.

But sweeping away these credits and deductions would raise relatively little money. Instead, the deductions that raise the most money are also the most popular, such as those for home mortgage interest, charitable contributions, and state and local taxes.

According to the Joint Committee on Taxation, the government could raise an additional $464 billion during the next five years by killing the home mortgage interest deduction.

Romney says he won’t do that. In a meeting with reporters and editors at the Columbus Dispatch Wednesday, he reiterated that position: “I have indicated we’ll keep the preferences for home mortgage interest deductions and … deductions for charitable contributions,” he said. “But that may be more limited for people at the high income level than it is for people at the middle income levels.’’

He also said he opposes eliminating the home mortgage interest deduction on second homes.

Instead, Romney has floated the idea of limiting the amount of money Americans could deduct from their taxes. He said Wednesday that “one would be to say everybody’s going to get $30,000 for deductions … whether it’s your home mortgage interest or charity or other things,’’ adding that the value of the deduction grows smaller for “people at the high end.’’

Critics complain that capping deductions is not the same as overhauling a complex tax code. David Kautter, a former partner at Ernst & Young and now head of the tax and accounting center at American University in Washington, D.C., said one of the stated goals of tax reform is making the law simpler, which isn’t accomplished by capping deductions.

“The second problem with a cap like that is that it is what I refer to as ‘geographically discriminatory,’ ’’ Kautter said. “The mortgage interest deduction and real estate tax deduction is greater in New York than in Wheeling, W.Va. It would affect different parts of the country differently.”

The other dispute revolves around whether lowering tax rates will — as both Romney and Portman argue — spark economic growth. Will McBride, an economist at the conservative-leaning Tax Foundation in Washington, said cutting taxes “actually works. We have a number of historical examples … There’s lots of evidence over the years to show tax rates matter for economic growth.’’

But Linden said the tax plan doesn’t add up and will unquestionably add to the deficit, joking that magic is needed to make the numbers work.

(Joe Vardon of the Columbus Dispatch contributed to this story.)