But with some notable exceptions, only so much can be delivered through the president’s pen if he is not using it to sign legislation. He cannot raise the minimum wage for most workers, overhaul the Social Security system, grant legal status to millions of undocumented immigrants, reorder spending and taxes, or even make necessary fixes to the health care law.

Illustrating how challenging it is to use executive orders in an expansive way, the White House refused to say how many workers might gain under the new wage policy, and Republicans, while criticizing the move, played down its impact. At the same time, anyone who succeeds him can use the stroke of a pen to undo Mr. Obama’s actions just as Mr. Obama did to some Bush-era policies one day after his inauguration in 2009.

“There is nothing like legislation,” said Rahm Emanuel, the Chicago mayor, the president’s first chief of staff and a former House member who advocates the strong use of executive power. “But given the challenges that are mounting, the country cannot afford Congress to go M.I.A.”

When it comes to Congress, the formula for success in dealing with a balky opposition continues to elude the White House except perhaps for a new opening with Republicans on immigration.