WASHINGTON » Four years ago, Barack Obama campaigned for president on a promise to cut annual federal budget deficits in half by the end of his term. Then came financial calamity, $1.4 trillion in stimulus measures and a maddeningly slow economic recovery.

Now, despite small annual improvements, the deficit for the fiscal year that ends Sunday will surpass $1 trillion for the fourth straight time. Against that headline-grabbing figure, Obama’s explanation — that the deficit he inherited is actually on a path to be cut in half just a year later than he promised if it is measured as a percentage of the economy’s total output — risks sounding professorial at best.

The fiscal imbalance on Obama’s watch, however much a result of economic and demographic factors beyond his control as well as his own policy choices, has increased the nation’s accumulated debt by about 40 percent and has saddled him with one of his biggest vulnerabilities. Facing off against Mitt Romney, Obama is on the defensive over deficits and debt nearly as much as he is over unemployment.

Dealing with deficits is the one major issue in which voters in polls regularly register more confidence in Romney than in Obama. It is also a flash point in the partisan war over the size and scope of government.

Romney and his running mate, Rep. Paul D. Ryan, chairman of the House Budget Committee, often campaign with digital debt clocks ticking off the rising liabilities. Their television advertisements highlight the issue; one appeals to women about the debt burden being left to their children.

Both Romney and Obama say that fixing the nation’s finances is a priority. But they approach it in very different ways.

Romney is proposing to reduce the deficit and encourage economic growth by substantially shrinking the government — unrealistically so, in the judgment of many budget experts — while further cutting taxes and increasing spending on the military. He would inject more private sector competition into Medicare to rein in the quickly growing costs of health insurance for older people and would limit Medicaid payments to fixed amounts to the states.

Obama wants to combine spending cuts and tax increases on upper-income households to close the fiscal hole without fundamentally reducing the role of government or altering the government guarantees at the heart of Medicare, Medicaid and Social Security. Those programs account for 40 percent of federal spending, and they will grow to half in a decade as more baby boomers claim benefits.

Romney has not put a figure on his deficit reduction target and has not fleshed out many of the details necessary to evaluate the long-term effects of his plan, but he says he would balance the annual budget in eight to 10 years. Obama’s most recent budget proposal called for $5.3 trillion in deficit reduction over the next decade.

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 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 Romney’s plan over the next decade, from 73 percent today. Under 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 to 70 percent.

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 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 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.

But Romney has said he would not raise taxes on the middle class. His chief economic adviser, R. Glenn Hubbard, the dean of the Graduate School of Business at Columbia University, said Romney would shrink his tax cuts before he would break that promise. The Romney plan also counts on economic growth to generate some new revenue to pay for tax cuts.

Because Romney would delay his Medicare changes for a decade to exempt current beneficiaries and those nearing eligibility, the savings would not help him keep his promise to balance the budget in eight to 10 years. That goal is two decades sooner than Ryan would reach balance in his House budget, indicating how much deeper Romney would cut domestic programs than Ryan would.

Romney has characterized his call for the repeal of Obama’s health care law as a budget saving measure, but the Congressional Budget Office has said that repeal would add $800 billion to the deficit over the next decade. Romney’s main proposal for reducing deficits in the short run is to cap all spending by the end of his term at a level equal to 20 percent of gross domestic product, the average for the 30 years before the recession, before spending on stimulus measures, unemployment aid and retiree benefits helped drive spending to the current 23 percent.

But long before the recession, forecasts had federal spending rising above 20 percent of gross domestic product in this period, largely a result of the pressures of an aging population. So the Obama camp argues that a 20 percent cap is unworkable.

More likely to get squeezed, whoever is elected, and certainly under Romney, is the wide range of domestic discretionary programs, covering education, science, law enforcement, veterans’ care and more.

These programs, which Congress finances annually, get a relatively small and declining share of the federal budget as spending grows for entitlement programs, the military and interest on the debt. The bipartisan deficit deal last year called for cuts of more than $1 trillion over 10 years. Many analysts doubt that Congress can agree to those reductions, yet Romney’s cuts would come on top of them.

Obama’s plan, which would seek to balance spending cuts and tax increases, has been attacked from opposite sides — from conservatives for raising taxes and from budget watchers who agree with Hubbard that the president cannot finance the government he wants simply by increasing taxes on the rich.

"We’re going to have to raise taxes more than the president has proposed, and on a broader swath of taxpayers," Reischauer said.

Obama’s budget "comes out in a better place than we are now," said Robert L. Bixby, the executive director of the Concord Coalition, a budget watchdog group. "But it’s not like it’s full of bold proposals. And it doesn’t add up to a sustainable outlook."

© 2012 The New York Times Company