We have come to believe a story about the deficit that is largely not true.

It’s a comforting story, to be sure. It holds the promise of a painless solution, because it suggests that the country’s huge looming deficits are not really our fault. Instead, they seem to stem from weak-willed politicians, wasteful government programs that do not benefit us and tax avoidance by people we have never met.

In truth, the coming deficits are a result, above all, of the fact that most Americans are scheduled to receive far more in Medicare benefits than they have paid in Medicare taxes. Conservative and liberal economists agree on this point. After Medicare on the list of big, growing budget items come Social Security and the military.

The three programs are roughly as popular as tax increases are unpopular – which is precisely why solving the deficit problem will be so difficult.

The new Times/CBS News poll highlights the problem, by asking more specific questions about taxes and spending than many previous polls have. (See questions 33 through 45 here.) Not surprisingly, when given a straight-up choice between broad spending cuts and tax increases, Americans say they would prefer to reduce the deficit mostly through less spending. It’s not even close: 62 percent for spending cuts, 29 percent for tax increases.

A few questions later, though, our pollsters offered a different choice. Would people rather eliminate Medicare’s shortfall through reduced Medicare benefits or higher taxes?

The percentages then switch, becoming nearly a mirror image of what they had been. Some 64 percent of respondents preferred tax increases, while 24 percent chose Medicare cuts. The same is true of Social Security: 63 percent for higher taxes, 25 percent for reduced benefits.

Herein lies the political problem. We want to cut spending. We just don’t want to cut the benefits that the spending pays for.

“The United States faces a fundamental disconnect between the services that people expect the government to provide, particularly in the form of benefits for older Americans,” Doug Elmendorf, the director of the Congressional Budget Office, has said, “and the tax revenues that people are willing to send to the government to finance those services.”

In fact, the Congressional Budget Office’s grim forecasts assume, realistically or not, that almost all forms of spending other than retirement spending will grow more slowly than they have been growing. So even if Congress does become more disciplined about the spending it controls, the big, looming deficits will still arrive. They come almost entirely from Medicare, Medicaid and Social Security. (The current deficit — a product of the wars in Iraq and Afghanistan, the Bush tax cuts, the new Medicare drug benefit, the Great Recession and the stimulus program – is indeed likely to shrink as the economy recovers in coming years.)

From a purely economic perspective, the deficit remains a manageable problem. Some smaller government programs truly are wasteful and could stand to be cut. Relatively modest changes to Social Security – like raising the eligibility age or starting to subject some income above $106,800 to the Social Security tax – would eliminate its shortfall. Military spending could be cut significantly and still be much greater than in the past or much greater than in any other country.

Even Medicare and Medicaid don’t look intractable. After all, every other country in the world, including some that get medical results as good as ours over all, spends far less on health care than we do. It is possible.

And if you really want to find reasons for optimism, you can do so in the public opinion data. When Americans are given a set of realistic choices, they are perfectly willing to prioritize.

The poll’s respondents, for example, said they would rather cut military spending than Medicare or Social Security (and several bipartisan groups have made specific suggestions for doing so). If Medicare and Social Security must be changed, people prefer increasing payroll taxes on high-income households or raising the Medicare eligibility age – not cutting back on Social Security paychecks or Medicare treatments. Within the tax code, a reduced tax break for mortgage interest looks more palatable than a reduced tax break for health insurance.

But none of these narrow, technocratic questions is the first one that needs to be answered. The crucial question today is, simply: Would you rather have your taxes increased or your Medicare and Social Security benefits reduced? “All of the above” is a reasonable answer. “None of the above” is not.

If there any politicians who can get us to accept this reality, they haven’t done so yet.