GIVEN THE the many competing demands on the nation’s limited resources, how high should increasing Social Security benefits be on the priority list? Very high indeed, according to Democratic Party activists, who regard fatter checks for the elderly as a hallmark of what true progressives believe. That’s why both Hillary Clinton and Sen. Bernie Sanders (I-Vt.) have embraced a version of the proposal in their campaigns for president.

Now comes President Obama with a declaration Wednesday in favor of “increas[ing] its benefits so that today’s retirees and future generations get the dignified retirement that they’ve earned.” Thus did Mr. Obama finally capitulate to Democratic critics who never quite forgave his previous willingness to trim Social Security cost-of-living increases; he’s helped to cement the new “progressive” orthodoxy.

Except that there would not necessarily be anything progressive about an across-the-board Social Security increase, even one paid for by imposing the payroll tax on wages and salaries above the current $118,500 maximum, as the Democrats suggest. The program requires that much of what higher earners pay in higher contributions would have to be returned to them as higher benefits. An analysis by the Third Way think tank of Mr. Sanders’s Social Security-boosting plan, the most aggressive, found that it would confer five times more money on the top 20 percent of earners than on the bottom 20 percent. Ms. Clinton, for her part, has proposed more limited benefit expansion, for widows and for those who took significant time out of the paid workforce to care for children. Even that proposal, however, is not targeted to the neediest in each category.

Not only does Social Security compete with other spending priorities; there are also competing priorities within the program itself. Specifically, revenue spent enhancing benefits cannot be used to build up the Social Security Trust Fund, currently headed for depletion by 2034. By all means, impose payroll taxes on more earnings, as all Democrats now suggest — including Mr. Obama, though he never formally proposed such a tax increase during his presidency. Even top earners have only finite resources, however; if you tax them more for Social Security, it will be harder to tax them more for other pressing needs. Additional payroll taxes should be used to extend the trust fund, thus stabilizing overall federal finances and preserving “fiscal space”; benefit increases, if any, should be targeted to the very poorest elderly.

In truth, the elderly as a whole are not the neediest group in our society; far from it. People 65 and over are less likely than the general public to live in poverty — and only half as likely to live in poverty as children under 18, according to the Census Bureau. They have higher average income (from all sources) than their counterparts in all but one other industrialized democracy, according to the Committee for a Responsible Federal Budget. Some 44.8 percent of those 65 and up are “satisfied” with their financial situation, roughly twice the level of comfort of all other age cohorts, according to the National Opinion Research Center’s 2014 General Social Survey. Yet in 2011, the federal government spent six times as much on the elderly as it did on children. Children can’t vote.

The President called for an expansion of social security during remarks at Concord Community High School in Elkhart, Indiana. (The White House)