WASHINGTON — For all the ambition of President Obama’s plan to significantly expand the number of Americans eligible for overtime pay, the proposal falls well short of helping substantially increase middle-class wages, its chief advertised benefit.

“This rule will raise wages and lead to better lives for millions of working people in the lower middle part of the labor market,” said Damon Silvers, policy director of the A.F.L.-C.I.O. “Of course it’s necessary, but it’s not sufficient. Not by a long shot. Wage stagnation is a problem for 90 percent of workers.” The rule would raise the salary threshold for workers to automatically receive time-and-a-half pay after working 40 hours in a week, lifting it from its current level of $23,660 to $50,440, where it last stood in the mid-1970s in terms of purchasing power. The new threshold would also rise over time so that inflation does not significantly erode its value.

“This proposed overtime rule goes to the heart of what it means to be middle-class in America,” Labor Secretary Thomas Perez told reporters Tuesday. As the threshold for overtime pay has “atrophied,” he said, “it’s no coincidence that so too has the middle class’s ability to get ahead and stay ahead.”

Given the political hurdles, the White House and its allies argue, the overtime rule represents a major advance.