Rep. Paul Ryan (R-Wis.) accused President Obama last week of setting the nation on an “unsustainable” path that would endanger “our kids and grandkids.” Obama, in turn, alleged this week that Ryan and Republican front-runner Mitt Romney were trying “to impose a radical vision on our country . . . thinly veiled Social Darwinism.”

It was a familiar punch-counterpunch over the problem of the nation’s rocketing debt. Yet amid the rhetoric, it was easy to overlook a fundamental question:

Why can’t America’s leaders, at the helm of such a wealthy country, find a solution that both puts the nation on a long-term path to financial security and preserves the vast array of vital services government provides?

Obama attempts to strike the balance in the short term, in an approach that largely maintains government as it is today. But he hasn’t presented a plan that would protect future generations from a fast-growing national debt.

Ryan offers a strategy that he says would put an end to the nation’s debt problems. But it comes at a great cost to the types of government programs Americans have come to rely on.

Different priorities

The reason neither man has found the sweet spot — which both stabilizes the debt and preserves key programs — has in part to do with political taboos. Obama has yet to put forward a plan that fully addresses the long-term costs of Medicare, a primary driver of the nation’s debt. Medicare’s costs will be pushed higher by waves of retiring workers. Although he wishes to raise taxes on the wealthy, he has pledged to leave people earning less than $250,000 alone, depriving the government of a potential source of substantial revenue.

Ryan, Romney and many Republicans, however, refuse to raise taxes at all. To the contrary, they wish to reduce rates, with wealthy Americans being the biggest beneficiaries of those reductions. Such an approach requires deep cuts to the nation’s safety net.

“The president has to be more realistic about raising taxes more across the board on a broader group of people if he’s going to maintain spending at the levels he’s talking about,” said Roberton Williams, a senior fellow at the nonpartisan Tax Policy Center. “On the other side, the Republicans are going to have to realize that not increasing taxes requires the very, very large cuts in spending that disproportionately benefits low- and middle-income households.”

The clash of approaches to addressing the national debt will be a central theme in this year’s campaign, and it could come to a head soon after the election, when current law calls for sharp cuts to defense and domestic programs and the expiration of a host of tax cuts that benefit virtually every American. Congressional aides have dubbed the Jan. 1 deadline, “Taxmaggedon.”

An agreement last summer to tame the debt already is slicing nearly $1 trillion from domestic and defense appropriations over the next decade.

To find savings, Ryan’s budget overhauls federal programs in ways that he says will reduce costs significantly. According to the left-leaning Center for Budget and Policy Priorities, 62 percent of his budget cuts come from low-income programs such as Medicaid and food stamps.

But the cuts, over time, would virtually obliterate domestic discretionary spending, which includes basic science research and education.

“This is the seed corn for the future,” said G. William Hoagland, a former top budget staffer for Senate Republicans. “By squeezing and cutting in this particular area, you end up really threatening the long-term investments that we need to make.”

Ryan, in a statement, said his budget tries to prioritize critical government programs and reform the safety net while reducing spending to avoid a “debt-fueled economic crisis” in which society’s most vulnerable would be hurt “the first and the worst.”

Obama’s strategy allows him to preserve government’s role in society but also limits what he is able to do to fix the debt problem.

His proposal to raise taxes on top earners provides some revenue to pay for benefits and domestic programs. And his health-care law, if it survives the Supreme Court challenge, might rein in some costs.

But he is not seeking to increase taxes on 98 percent of the population, and he is proposing, in the words of his budget, only “modest adjustments” to the nation’s entitlement programs.

In part as a result, Obama’s budget documents show that the debt will rapidly climb upward after 10 years of stability.

The White House says it has embraced a balanced approach that has already reduced the long-term deficit and produced a plan that would keep the debt stable and make a contribution to addressing long-term problems. And that’s been done without raising taxes on the middle class, a pledge the president intends to keep, officials say.

“In the future you’re going to need additional work on a bipartisan basis,” said Jason Furman, principal deputy director of the National Economic Council. “The president has shown he is willing to do that.”

Long-range projections

Long-range budget projections are based on a complex set of guesses about economic growth and other factors, making it hard to know what will really happen in the future. That said, broad patterns are clear.

At the end of 2011, the U.S. public debt amounted to 67.7 percent of gross domestic product, a common measure of debt stability. Economists say high debt levels can increase the risk of financial crises.

The average debt-to-GDP ratio of the postwar period was about 40 percent.

The Committee for a Responsible Federal Budget, a nonpartisan group that advocates a big deficit-reduction package, has analyzed the trajectory of debt under the Obama plan and the Ryan plan, based on assumptions about the future provided by the president and the congressman.

Obama’s budget would stabilize the debt at 76.5 percent of GDP over the next 10 years. But the debt would soon start to march upward, climbing to 87.4 percent in 2032, 107.7 percent in 2042 and so on.

By contrast, Ryan’s plan drives the debt-to-GDP ratio lower. It would be 62.3 percent in 2022, 49.6 percent in 2032 and 29.1 percent by 2042.

One option that would help preserve benefits and keep the debt stable, though elevated, for at least two decades is to allow George W. Bush-era tax cuts for the upper and middle classes to expire, according to the Congressional Budget Office.

If that happened, tax revenue as a percentage of the overall economy would rise far above historic averages, the CBO says.