Most ominously, independent voters  who embraced Mr. Obama’s presidential campaign and are an increasingly critical constituency  seemed to have fled to Mr. Brown in Massachusetts, as they did to Republicans in races for governor in Virginia and New Jersey last November. It is hard not to view that as a repudiation of the way Mr. Obama and Democratic Congressional leaders have run things.

Image The mood was grim among Martha Coakley’s supporters as the results came in to their hotel in Boston. Credit... Yana Paskova for The New York Times

“This is a giant wake-up call,” said Terry McAuliffe, the former Democratic National Committee chairman who lost a bid for the Democratic nomination for governor in Virginia last year. “We have to keep our focus on job creation. Everything we have to do is related to job creation. We have to do a much better job on the message. People are confused on what this health care bill is going to do.”

Even before the polls closed, the White House was suggesting the outlines of a recovery strategy, a combination of a more populist tone and an embrace of greater fiscal responsibility.

Mr. Obama has signaled that he intends to take a more populist stance on financial regulation legislation in Congress, seeking to position Democrats as defenders of the people against Wall Street, and to cast Republicans as defenders of bonus-laden bankers. And on Tuesday night, the White House brokered a deal that could lead to a bipartisan commission to recommend spending cuts and tax increases to address the nation’s fiscal condition. For months, Mr. Obama’s advisers had warned that the perception that budget deficits and the national debt were spiraling out of control was alienating independent voters already turned off by partisan battling.

David Axelrod, a senior adviser to Mr. Obama, said he did not view the results as a repudiation of the White House’s agenda, but he acknowledged that the administration needed to do a more effective job of signaling concern about the problems gripping Americans.

“We are the party in power, and as such there’s an element of responsibility assigned,” he said. “I think people need to know that their challenges and their concerns are the focus of our work every day.”