President Obama and his rival Mitt Romney spent a good part of their first debate arguing about the effects of their tax plans on the nation's gaping deficits. It made for good political theater, but neither man was completely honest about the sacrifices that will be asked of the American public.

During Wednesday's debate, Obama and the former Massachusetts governor traded barbs over Romney's promise to lower tax rates for ordinary Americans, a promise Obama alleged would add $5 trillion to the deficit. Romney denied that, and he promised he would revamp the tax code without raising taxes and without adding to deficits.

Romney insisted the revenue lost from his proposal to cut existing tax rates by 20 percent would be made up by closing loopholes in the tax code, which aren't really loopholes but rather deductions that Americans have been accustomed to receiving during the calculation of what they owe in income taxes. Tax experts, however, don't see how this happens without steep cuts to popular deductions, such as those for charitable giving and mortgage interest. Neither Romney nor Obama spelled out what sort of tax breaks they're prepared to tackle.

"Nobody wants to give the American public the bad news that there is only one way to deal with our budget deficit, and that's we're going to have to raise taxes and cut spending," said Roberton Williams, a senior fellow at the Tax Policy Center, a joint effort of the centrist Urban Institute and the center-left Brookings Institution.

Many analysts think it virtually impossible to have comprehensive tax reform without a parallel effort to reduce debt and deficits as part of a long-term political deal. Romney envisions tax reform and deficit reduction independent of each other.

"We did it in 1986, but in this environment I can't see how. I think that dynamic has been pretty well established," said Steve Bell, who was chief of staff on the Republican-led Senate Budget Committee during the last comprehensive tax overhaul. He is now senior director of economic policy at the Bipartisan Policy Center, a think tank that tries to narrow political differences on legislation.

The president's own National Commission on Fiscal Responsibility and Reform, whose recommendations for deficit reduction he largely ignored, called in December 2010 for closing tax loopholes as part of a revamp of the tax code, and using those revenues to narrow the deficit.

Romney has embraced the commission's call for lower tax rates with fewer deductions, but he hasn't spelled out what he would end or scale back.

"He's got half a plan -- he's got the goodies part of it, the fun part, the tax cuts. But he doesn't have the broccoli part," said Williams. "He offers the dessert, but doesn't tell you that you have to eat your broccoli, too."

Obama hinted at broccoli, suggesting some tax increases were needed but not offering a lot of detail on how those would fit within a comprehensive reworking of the tax code and deficit reduction.