According to the Center on Budget and Policy Priorities, if Mr. Romney spared those 55 and over from any changes to Medicare or Social Security, as his campaign has promised, spending on everything else would have to be cut by more than $6 trillion from 2014 to 2022. The center did not specify how this would affect the young. But a repeal of health care reform would drastically reduce health benefits. The budget for Medicaid, which is the biggest federal program serving children, would be cut by almost $2 trillion over 10 years.

There is good reason to be worried about our long-term budget deficits. They are indeed projected to be huge — driven mostly by the growing health care spending of an aging population. Medicare will absorb about 6.7 percent of the nation’s economic output by 2037, up from 3.7 percent today, under the most likely situation laid out by the Congressional Budget Office.

Though President Obama and Mr. Romney acknowledge the American economy can’t afford that, they have each devoted a big chunk of their campaigns to convincing seniors that their benefits will not be compromised. Social Security and Medicare “are bedrock commitments that America makes to its seniors,” President Obama said in a speech to the AARP last month. The Republican vice-presidential candidate, Paul Ryan, told the same gathering, “Medicare is a promise, and we will keep it.” The generation whose taxes will be footing the bill in 2037 doesn’t get the same type of commitment.

Isabel Sawhill, a senior fellow at the Brookings Institution and a co-director of its Center on Children and Families, argues it is time to reconsider the intergenerational deal that has held since Social Security’s inception in the 1930s. The assumption behind it was that working-age Americans could support their children and every senior would be able to retire at age 65.

Today, this compact is under strain. Health spending has skyrocketed while middle-class wages have failed to keep up with the cost of living. The old are living longer and collecting more benefits than before. Even under new measures of poverty that account for seniors’ high medical spending, poverty rates among children have surpassed deprivation among the old. Seniors, Ms. Sawhill suggests, could shoulder more costs so that more of the money from working Americans could be devoted to the young.

There are ways to do this while still protecting the most vulnerable seniors. Social Security benefits could be indexed to slow their growth for high-income seniors. Wealthier retirees might bear a larger share of their medical expenses. The retirement age could be raised.