He rejected the suggestion that Mr. Obama, who forced Republicans to accept higher taxes on the wealthy after re-election, has been too passive. “The notion that there’s some sort of easy leadership play that he hasn’t called yet that would unlock gridlock, that’s not a very sophisticated analysis,” Mr. Plouffe said.

Second terms have long vexed presidents, whether it was the Iran-contra affair for Ronald Reagan or impeachment for Bill Clinton. Much as Mr. Obama failed to win his first big post-inaugural priority in gun control, President George W. Bush saw his effort to revamp Social Security in his fifth year go nowhere. With violence spiraling in Iraq, Mr. Bush found it hard to regain traction.

Yet presidents have made breakthroughs in their second term amid Congressional investigations. Reagan signed a nuclear-arms treaty with the dying Soviet Union, and Mr. Clinton balanced the budget. Mr. Bush defied broad opposition to a troop surge in Iraq, fueling a turnaround there.

For Mr. Obama, the sharp drop in the projected deficit, announced Tuesday by the Congressional Budget Office, served as a reminder that if he finishes his term with a healthier economy, it may matter more to his legacy than this week’s setbacks.

Still, the latest furors could harden an impression of an Obama presidency that has expanded the reach of government further than many Americans would like. And they can undermine a powerful tool of the presidency, the ability to focus public attention.

Mr. Obama recognized the dynamic while a senator, telling aides that a president could drive just 15 to 20 percent of the public agenda; the rest of the time, he had to react. In that light, aides say, Mr. Obama maintains his famed equanimity and, free of campaign pressures, takes a longer view.

“Being in office for nearly four and a half years gives the president some perspective — it helps separate the signal from the noise,” said Dan Pfeiffer, a White House senior adviser. “When you have dealt with real life-and-death problems, the political ones seem much smaller and affect you less.”