Advocates for the change immediately hailed the decision.

“The president said he wanted to go big here and he did,” said Jared Bernstein, a former White House economist who co-wrote an influential report on the benefits of expanding overtime pay after leaving the administration in 2011. “I can’t think of any other rule change or executive order that would lift more middle-class workers.”

At least two candidates for the 2016 Democratic presidential nomination, Gov. Martin O’Malley of Maryland and Senator Bernie Sanders of Vermont, have urged action on the overtime regulations.

Conservatives and business groups have bitterly opposed the idea, warning that it will cost jobs. The National Retail Federation, a trade group, has argued that expanded overtime will “add to employers’ costs, undermine customer service, hinder productivity, generate more litigation opportunities for trial lawyers and ultimately harm job creation.”

The rule, which would most likely be completed in 2016, would give workers whose salary is between the current threshold and the new threshold a raise if they work more than 40 hours a week. Advocates on both sides of the issue expect the policy to be challenged in court and perhaps in Congress as well.

Republicans could, for example, attach a so-called rider undoing the change to must-pass appropriations measures later this year.