Polls show that most Americans are opposed to raising the federal debt ceiling. Even when the Pew Research Center included the consequences in its question — a national default that would damage the economy — slightly more people were against raising the ceiling than were for it.

How could this be? Above all, I think it reflects a desire to return to the good old days. Not so long ago, nobody was talking about tax increases or Medicare cuts, and the federal budget seemed to be in fine shape. If only we could get back to the past — get spending under control, as the cliché goes — we’d be O.K. The debt ceiling, with its harsh finality, offers the chance.

Unfortunately, this nostalgic view depends on a misunderstanding of the budget. It imagines a budget in which the United States indefinitely has the world’s highest medical costs, its largest military, an aging population and, nonetheless, taxes that are among the world’s lowest. Economists have a name for that combination: a free lunch.

Free lunchism is ultimately the problem with the no-new-taxes pledge that so many politicians have adopted. A refusal to raise taxes, no matter how principled, cannot take us back to the good old days. It would instead lead to a very different American society. For taxes to remain where they are, Washington would need to end Medicare as we know it, end Social Security as we know it, severely shrink the military — or do some combination of the above.

“We cannot repeat the past when it comes to the federal budget,” Douglas Elmendorf, director of the nonpartisan Congressional Budget Office, recently wrote. “The aging of our population and the rising cost of health care have changed the backdrop for federal budget policy in a fundamental way.”

The most important part of the recent Republican budget plan, written by Representative Paul Ryan, was that it acknowledged this reality (in its details, if not its packaging). It called for no tax increases. To make the numbers come close to adding up, the plan also called for eliminating the current Medicare and replacing it with a system in which the elderly would buy less generous private insurance plans. Such is the price of no new taxes.

Early indications are that Americans don’t like Mr. Ryan’s plan all that much. In upstate New York this spring, a Democrat won a typically Republican House district by campaigning relentlessly against the plan. National polls show huge majorities favor keeping Medicare and Social Security in something approaching their current form — much larger majorities, tellingly, than oppose an increase in the debt ceiling.

In the near term, Congressional Republicans have decided to play down the Ryan plan. Most continue to oppose new taxes, without going so far as to explain the consequences. They will have little trouble sticking to that position through the current debt ceiling fight, because the deficit does not need to be solved immediately.

Eventually, though, drawing up a credible deficit plan with neither Ryan-like cuts nor higher taxes will be impossible. And you can already see the start of a potential Republican compromise.

It revolves around raising taxes, on net, by shrinking corporate or individual loopholes. The country’s highest-ranking Republican, John Boehner, the speaker of the House, signaled his openness to such a deal last week. (Mr. Boehner abandoned the deal under pressure from Representative Eric Cantor, the No. 2 House Republican and a Tea Party ally.)

Stalwart Republican economists — like Martin Feldstein, a chairman of the Council of Economic Advisers under Ronald Reagan, and Gregory Mankiw, who held the same job under George W. Bush — also favor raising taxes by closing loopholes. So did most of the Republicans from the bipartisan Simpson-Bowles deficit commission, including Senator Tom Coburn of Oklahoma, Senator Mike Crapo of Idaho, former Senator Judd Gregg of New Hampshire and David Cote, the chief executive of Honeywell.

One obvious compromise along these lines would follow the outline sketched out by the Simpson-Bowles plan. Marginal tax rates could actually fall. But the closing of loopholes would more than make up for the loss in revenue from lower tax rates.

Conservatives might accept the deal, partly because it would satisfy their longtime desire for a simpler tax code with lower rates and partly because spending cuts would still make up the bulk of any deal. Liberals might accept the deal because tax loopholes disproportionately benefit the wealthy, and a simpler code — even one with lower rates — could be more progressive.

The mortgage interest deduction, for example, saves more than $5,000 a year for the typical household in the top 1 percent of earners. Most middle-income households don’t benefit from the deduction at all, because they instead claim the standard income tax deduction. And the mortgage deduction is the second-largest tax break for individuals, costing about $80 billion a year, more than the budgets for the Education Department and Justice Department combined.

Yet despite all the substantive arguments for such plans, I still wonder whether one of them is the most likely outcome.

The truth is, closing loopholes has much stronger support among economists and columnists than it does among voters. Only 23 percent of Americans benefit from the mortgage deduction, but 93 percent support it. Other big breaks, like the exclusions for health insurance and 401(k) contributions, are popular, too. On the corporate side, Eric Toder of the Urban Institute has pointed out that the biggest breaks also tend to be popular, like the credit for research and development.

So what kind of tax increases do Americans support? The old-fashioned kind. Seventy-two percent support raising taxes on income above $250,000, according to a recent New York Times/CBS poll, and a large majority likewise favor raising Social Security taxes on the affluent.

In the end, the most likely tax increase may be the one that’s already on the books. On Jan. 1, 2013, all the Bush tax cuts — on the affluent and nonaffluent alike — are set to expire, which would solve roughly one-quarter of our long-term deficit problem. If Republicans have their way, all the tax cuts will be extended. If the Democrats have their way, most of them will be.

But if the two parties each control a branch of government after the 2012 elections, neither may be able to get their way. Instead, they would have to compromise — or a stalemate would cause the Bush tax cuts to disappear. After the last few days, a stalemate doesn’t seem like such a bad bet.

E-mail: leonhardt@nytimes.com; twitter.com/DLeonhardt

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