WASHINGTON » They have had their fleeting moments on cable television. Their closed-door run-ins with Speaker John A. Boehner spill occasionally into the pages of Capitol Hill newspapers. But outside their districts, and sometimes even within them, few have heard of the conservative cadre of House Republicans who have led the charge to shut down the government.

In contrast to 1995, when Speaker Newt Gingrich led his band of "revolutionary" Republicans into the last battle that shuttered the federal government, this time a small but powerful group of outspoken conservative hard-liners is leading its leaders – and increasingly angering a widening group of fellow Republicans.

"We’ve passed the witching hour of midnight, and the sky didn’t fall, nothing caved in," said Rep. Steve King, R-Iowa, who still believes Republicans can achieve "the end of Obamacare." "Now the pressure will build on both sides, and the American people will weigh in."

King is part of a hard-core group of about two dozen or so of the most conservative House members who stand in the way of a middle path for Boehner that could keep most of his party unified while pressuring the Senate to compromise. Their numbers may be small, but they are large enough to threaten the speaker’s job if he were to turn to Democrats to pass a spending bill that reopened the government without walloping the health law. Their strategy is to yield no ground until they are able to pass legislation reining in the health care law; if the federal government stays closed, so be it.

And they believe they are winning.

"It’s getting better for us," said Rep. Razl R. Labrador, R-Idaho. "The moment where Republicans are least popular is right when the government shuts down. But when the president continues to say he’s unwilling to negotiate with the American people, when Harry Reid says he won’t even take things to conference, I don’t think the American people are going to take that too kindly."

Rep. Jeff Duncan, R-S.C., also did not flinch.

"We feel strongly enough" to hold the line, he said. "I was elected in 2010. I feel Obamacare is shutting down America."

For nearly three years, Boehner has been vexed by an ungovernable conservative group made of up ideologically committed conservatives from safe House seats. The group has defied his leadership, rallied others to its cause and worn its gadfly status proudly. Earlier this year, the speaker disregarded them and passed three major bills that attracted only a minority of his party. Instead, he relied on Democratic votes to pass a budget plan that allowed taxes to rise on the rich, relief for victims of Hurricane Sandy and an expansion of the Violence Against Women Act.

That nucleus of that group has stuck in the leadership’s craw for some time. Rep. Justin Amash, R-Mich., has voted against Republican positions 136 times in his short stretch in Congress. Rep. Paul Broun, R-Ga., has voted no on Republican motions 84 times. Rep. Thomas Massie, a freshman from Kentucky, is rising in the pesky ranks with 91 no votes in nine months.

In March, Rep. Matt Salmon and David Schweikert, both Arizona Republicans, responded with a threat to bring down any bill that did not have overwhelming Republican support through procedural maneuvers. The speaker has refrained ever since.

But the influence of the group is sparking an internal backlash, as a growing band of moderate and institutional Republicans are demanding that Boehner stand up to the conservatives — to reopen the government and reach bipartisan accommodations in the future.

"You have somewhere between 180 and 200 Republican governance votes in the House, and going forward on this issue and many other issues, we’re going to have to find a coalition of Democrats to work with," said Rep. Charlie Dent, R-Pa., "and recognize there is going to be a few dozen people on the Republican side who just aren’t going to be there on a lot of these major governance matters."

With much of the government shut down, patience is wearing thin among some Republicans who see the maneuvering of the coalition of conservatives as counterproductive. In 2011, the hard-liners insisted on including a constitutional amendment to balance the budget in a House spending-cut bill, splitting the Republicans in a way that many believe led to fewer cuts in the final Budget Control Act than they would have had otherwise. In December, when they brought down the speaker’s proposal to let taxes rise on incomes over $1 million, Boehner was left with two choices: let the Bush-era tax cuts expire for everyone, or accept a bipartisan Senate plan that raised taxed on households earning over $400,000. He chose the latter.

"I’m not suggesting their motives are not legitimately felt, but you get to a point where we can accomplish something here, but we’re watching the speaker constrained on what he can deliver, a practical promise from a united House," said Rep. Patrick Meehan, R-Pa. "We retreat from a position of strength and accept something that’s worse."

Now, many Republicans believe conservative demands to inflict real damage to the health care law is letting slip away the chance to make more realistic changes to the law, like a repeal of its tax on medical devices.

"They have never followed any leadership plan, and now all of a sudden the leadership has adopted their plans and we’re fully implementing their strategy and plan, which is I think is actually a lack of a strategy," said Devin Nunes, R-Calif.

House Republicans were seething Tuesday after two of the most ardent conservatives, Broun and Phil Gingrey, also R-Ga., voted against a House Republican bill that linked further government funding to a measure to deny federal subsidies to members of Congress and their staff, who must purchase their health insurance on the health law’s new insurance exchanges. The proposal is unpopular with staff members who would have to cover the full costs of their insurance, unlike most public and private sector jobs where employers pick up part of the premiums.

They said the vote was unexpected because two weeks ago Gingrey stood at a closed-door party meeting and said members concerned about hurting their staff were misguided, since they would just go to lobbying firms "downtown" and make a half-million dollars a year.

"The congressman made a pledge that he would not vote for a continuing resolution that funded Obamacare. That was the compelling factor in his vote last night, " said a Gingrey spokeswoman, Jen Talaber.

The conservatives remain resolute against compromises, even some embraced by Republican leaders. Rep. John Fleming, R-La., said he could not accept a repeal of the health law’s tax on medical devices as a concession to reopen the government.

"That could be bad because it could improve a bad bill," he said. "And while it’s a terrible tax, removing a tax to make what is really an atrocious bill to the economy slightly better, I’m not sure that’s a good idea."

To many Senate Republicans, the House’s position has now become mystifying.

"I can’t blame them for anything other than being sold a line that wouldn’t work, seeing the outside support and saying ‘maybe, maybe, maybe,’" Sen. Richard M. Burr, R-N.C., said of House conservatives. "Well, you know that train only in a children’s story actually gets to the top of the hill."

© 2013 The New York Times Company