But long-term projections are notoriously unreliable. And in any case, budget analysts say that if the nation’s goal — at a moment when the economy is still shaky — is to start moving seriously toward fiscal balance, neither approach is likely to prove equal to the problem.

Robert D. Reischauer, a former head of the Congressional Budget Office, expressed the consensus of many independent analysts, saying, “The proposals by Romney are politically unachievable, and the president’s proposals, while achievable, are too modest.”

The plans of both, analysts say, would leave the public debt continuing to rise over the next decade as a percentage of gross domestic product, the measure that economists favor. Though Mr. Romney’s plans are more difficult to judge, given his lack of specifics, by some analyses he would do less to reduce annual deficits in that time than the president would, considering his position against raising taxes, his call to increase military spending and the fact that his proposals to remake Medicare — the largest contributor to long-term deficits — would not kick in until after 2022.

One analysis, from the Committee for a Responsible Federal Budget, estimated that the debt would grow to at least 86 percent of gross domestic product under Mr. Romney’s plan over the next decade, from 73 percent currently. Under Mr. Obama’s policies, the debt would increase slightly after a decade, to about 77 percent of gross domestic product, according to the Congressional Budget Office. Many analysts say that a nation’s debt should not exceed 60 percent to 70 percent.

Mr. Romney wants to cut taxes by $5 trillion on top of the Bush-era rates and keep military spending at a level requiring $2.3 trillion more than projected in the decade. But he also pledges to offset those costs to avoid adding to deficits, paying for the tax cuts by closing tax breaks and for the military spending by cutting domestic programs. In effect, he has challenged himself to find $7 trillion in savings before he even turns to deficit reduction.

“That means you’ve got to make really big cuts in those areas that we have got to invest in to be competitive in a knowledge-based global economy: education, infrastructure, research,” said Erskine B. Bowles, a Democrat who helped lead a bipartisan debt commission for Mr. Obama in 2010. “Also, you’ve got to make really big cuts in the income-support programs that take care of the disadvantaged.”

Independent analyses have also outlined the difficulty Mr. Romney would face in finding enough savings in the tax code to pay for his tax cuts. For all the talk of loopholes and tax dodges, the real money is in the popular deductions and credits — for employee health benefits, mortgage interest, charitable donations, state and local taxes, child care and college tuition — that benefit many middle-income Americans.