It is a measure of Mitt Romney’s inadequacies as a candidate that he has not been able to turn his latest gaffe — his dismissive reference to the 47 percent of Americans who “are dependent upon government” — into a teachable moment and a campaign advantage. Stigmatizing almost everyone with a federal benefit is not just bad politics. It’s the worst sort of social stereotyping. But beyond Romney’s bluster lies a genuine problem. The fact that roughly half of Americans receive some government payment to which they feel morally entitled is a big part of our budget paralysis. It’s an inconvenient fact, but it’s still a fact.

Dealing with it ought to define the next president’s mission. Somehow, he must question the status quo without insulting the roughly 150 million Americans who receive federal benefits. Who deserves support and why? How much and under what conditions? Unless we ask these questions and find grounds for trimming some benefits, the budget impasse will continue and risk dangerous outcomes: a future financial crisis; crushing tax increases; or draconian cuts in programs (defense, research, highways) that aren’t payments to individuals.

This is arithmetic, as Bill Clinton might say. In 2011, payments to individuals were 65 percent of federal spending, up from 26 percent in 1960. America has created a welfare state, whether Americans admit it or not.

Actually, the share of people who receive federal benefits exceeds Romney’s 47 percent. Based on its Survey of Income and Program Participation (SIPP), the Census Bureau estimates that in mid-2011 — the latest available figures — the number of people with benefits came to 149.8 million, or 49 percent of the population. But this figure is too low, because SIPP doesn’t include several major programs (farm subsidies and college loans and grants). With these, the total probably exceeds 50 percent.

The big programs are well-known. In 2011, Social Security had 49.6 million recipients and Medicare 45.6 million, most of them overlapping. There were 5.2 million Americans with unemployment compensation and 3.2 million with veterans’ benefits. An estimated 107.2 million people received “means-tested” benefits available to those with low incomes. Medicaid had 80.5 million beneficiaries, food stamps 48.3 million and WIC (Women, Infants, and Children) 23.1 million. Among households with means-tested benefits, almost a third received three or more.

President Obama hasn’t controlled this spending or opened a debate about which benefits might — in the national interest — be curbed. His reluctance reflects conventional wisdom that questioning benefits is a political loser because it arouses the fears of millions of potential voters. But Obama’s expediency leaves Romney an opening, albeit a high-risk one. He could seize the moral high ground by posing the hard questions necessary for a future that does not penalize economic growth or overburden today’s young with taxes or debt.

This is an opportunity that Romney seems unwilling or unable to take, his brief engagement with Medicare aside. After the video’s release, he might have apologized for his clumsy language, while still urging voters to find a better balance between America’s past promises and future prospects. But he seems to lack the rhetorical skills to convince people why a rigid defense of the welfare state — effectively, Obama’s position — threatens the welfare of today’s young and tomorrow’s children.

Instead, Romney’s 47 percent comment implies that anyone who receives a federal benefit is a deadbeat. We’re talking about half the population! The social safety net is worth preserving; but it shouldn’t be sacrosanct. One test of presidential competence is the capacity to convince people that what’s good for the country is ultimately good for them, even if it involves short-term sacrifice. On the campaign trail, Romney is failing that test.