On Capitol Hill, it left the House speaker, John A. Boehner, and the top Republican in the Senate, Mitch McConnell, powerless to avert a debt crisis and government shutdown that damaged their party’s reputation. In part, that’s because so many top Republicans have been unwilling to risk angering voters and rank-and-file lawmakers by distinguishing legitimate grievances from contrived ones, lost causes from achievable goals.

“It’s always easier to stand up with the crowd and say, ‘You’re right, they’re all bums,”’ said Tom Cole, a Republican who represents a conservative Oklahoma district. In general, he added, “We’ve played into our worst instincts instead of our best.”

There’s nothing unusual about a president angering opposition members. When George W. Bush occupied the White House, Democrats fumed at government, too. Even today, Senator Bernie Sanders attributes the unexpected vibrancy of his primary campaign to “anger at the establishment” over stagnation in middle-class incomes.

But Republicans’ identification as the antigovernment party leaves its followers more prone to alienation. In a Pew Research Center poll before the 2006 midterm election under Mr. Bush, 28 percent of Democrats described themselves as “angry” at the federal government. In a similar poll four years later under Mr. Obama, 33 percent of Republicans called themselves angry.

When Pew examined public trust in government during recent presidencies, it found trust among Republicans in the Obama era lower than among either party for the past half-century; just 12 percent said they trusted government to “do what’s right” always or most of the time. And 52 percent of Republicans said Mr. Obama made them angry.