WASHINGTON — To many Americans, the war on poverty declared 50 years ago by President Lyndon B. Johnson has largely failed. The poverty rate has fallen only to 15 percent from 19 percent in two generations, and 46 million Americans live in households where the government considers their income scarcely adequate.

But looked at a different way, the federal government has succeeded in preventing the poverty rate from climbing far higher. There is broad consensus that the social welfare programs created since the New Deal have hugely improved living conditions for low-income Americans. At the same time, in recent decades, most of the gains from the private economy have gone to those at the top of the income ladder.

Half a century after Mr. Johnson’s now-famed State of the Union address, the debate over the government’s role in creating opportunity and ending deprivation has flared anew, with inequality as acute as it was in the Roaring Twenties and the ranks of the poor and near-poor at record highs. Programs like unemployment insurance and food stamps are keeping millions of families afloat. Republicans have sought to cut both programs, an illustration of the intense disagreement between the two political parties over the best solutions for bringing down the poverty rate as quickly as possible, or eliminating it.

For poverty to decrease, “the low-wage labor market needs to improve,” James P. Ziliak of the University of Kentucky said. “We need strong economic growth with gains widely distributed. If the private labor market won’t step up to the plate, we’re going to have to strengthen programs to help these people get by and survive.”