Rank-and-file Republicans are openly contemplating a coup against House Speaker John A. Boehner and his top lieutenants after a series of self-inflicted legislative fumbles and political defeats in the first weeks of the congressional session.

This week’s retreat from the standoff over Homeland Security Department funding and President Obama’s deportation amnesty was only the latest embarrassment for Republican leaders, who also have had to yank bills on abortion, border security and education after rebellions within their own party.

Rep. Andy Harris, Maryland Republican, conceded that running the conference was like “herding cats” but said that is not an excuse for failure.

“I’m still optimistic that leadership can herd the cats. But if they can’t, then I think there will be consideration about whether a new leadership team needs to be put in place,” Mr. Harris said.

The leaders have acknowledged stumbles at the opening of the congressional session, when Republicans took control of the Senate as well as the House and members had high expectations for advancing a conservative agenda. But leaders have insisted that they don’t need dramatic changes in how they run the conference, a Republican aide said.

House Majority Leader Kevin McCarthy, California Republican, prides himself on having an open-door policy and listening to members, but conservative lawmakers say the leadership team hasn’t been listening to them or their constituents.

“I don’t think they are listening to all the members,” said Rep. John Fleming, a member of a small band of lawmakers who formed the conservative Freedom Caucus and have been at the center of rebellions against the leadership.

He said the party leaders haven’t kept up with an increasingly conservative Republican base that is electing lawmakers who are more conservative.

“The problem is we are used to being in this moderate lane and the people, our constituents who are sending us here, are trying to move us over into the more conservative lane,” said the Louisiana Republican. “I think the struggle is that leadership has not yet picked up the trim line that they need to put out more conservative legislation to get better results.”

Supporters of the leadership team blame the dysfunction on conservatives such as Mr. Fleming, who they say sabotage good legislation by demanding perfect bills and ideological purity.

“Our problem isn’t leadership around here; it’s followership,” said Rep. Tom Cole, an Oklahoma Republican who is a close ally of Mr. Boehner.

“We have a group of people who, frankly, think they are always right and their leaders and the conference collectively are usually wrong,” he said. “It’s actually a fairly small group.”

Rep. Peter T. King, New York Republican, put it more bluntly: “I don’t consider them conservatives. I consider them anarchists.

“The whole party is going to suffer, not just the leadership, all of us are going to suffer if we can’t get more organized. But I don’t know if that group of about 35 wants to be organized. It’s almost as if they sit by themselves in the floor there — like a separate party, like in France or Italy where you have the rump parties out there,” Mr. King said.

Not all of the leadership’s dust-ups have been with conservatives.

The first blunder occurred with a bill that would ban abortion after 20 weeks of pregnancy, with an exception for cases of reported rape, incest or danger to the mother’s life. The leaders pulled the bill Jan. 21 to head off a revolt by some of the conference’s female and moderate members.

“We’re continuing to listen to everybody,” Mr. McCarthy said at the time. “We’re still planning on moving forward with the bill.”

The bill has yet to return.

A week later, a border security bill was pulled amid complaints from conservatives that it was too weak. The legislation is expected to return combined with other bills that beef up interior enforcement of immigration laws.

The third bill pulled off the floor would have rolled back parts of the No Child Left Behind Act, but conservatives balked that it didn’t do enough to get the federal government out of education.

Mr. Fleming said the education bill underscored the disconnect between Republican congressional leaders and voters.

“That’s the reason why there is frustration out there,” he said. “Time and time again, our constituents are telling us, ‘No, we don’t want federal mandating on school education. We want that left to the states.’ And yet somehow there are people who are making decisions up here who think that, ‘No, we just need to have just a little less federal control but not hand it over to the states.’”

Still, Mr. Cole said the Republican conference isn’t going to oust its leadership team.

“People really recognize that the problem is in the culture of the conference; it’s not with the leadership of the conference. So we have to work through this as a family and get to a point where we all — or at least 218 of us — are willing to work together,” he said. “If you can’t do that, you’re going to have a hard time accomplishing the things you said you wanted to do when you came here.”

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