WASHINGTON >> The hard-line stance of Republican House members on the government shutdown is generating increasing anger among senior Republican officials, who say the small bloc of conservatives is undermining the party and helping President Barack Obama just as the American people appeared to be losing confidence in him.

From statehouses to Capitol Hill, frustration is building and spilling out during closed meetings as Republicans press leaders of the effort to block funding for the health care law to explain where their strategy is ultimately leading.

"Fighting with the president is one thing," said Sen. Roy Blunt, R-Mo. "Fighting with the president and losing is another thing. When you’re in the minority you need to look really hard to find the fights you can win."

The complaints come from fervent opponents of the president’s health care overhaul, who say that the shutdown is overshadowing discussion of the problems associated with the law and ruining any chance for revising it.

"This is a huge distraction," said Gov. Bill Haslam of Tennessee. "Instead of that being the conversation, we’re talking about the government shutdown, and the average citizen can’t help but say the Republican Congress isn’t helping."

Members of Congress from swing areas and Republican governors appear the most vocal. At a meeting with House Republicans in the Capitol on Tuesday, Rep. Dave Reichert of Washington pointedly questioned what the end game is for the party, according someone who attended and spoke on the condition of anonymity because the session was supposed to be confidential.

Reichert, typically mild-mannered, represents a highly competitive suburban Seattle district. And on Wednesday at a private luncheon, several Senate Republicans — Dan Coats of Indiana, Ron Johnson of Wisconsin and Kelly Ayotte of New Hampshire — assailed Sen. Ted Cruz of Texas, who has led the movement to block funding for the health law.

Ayotte was especially furious, according to two people present, and waved a printout from a conservative group friendly to Cruz attacking 25 of his fellow Republican senators for supporting a procedural vote that the group counted as support of the health law.

Ayotte asked Cruz to disavow the group’s effort and demanded he explain his strategy. When he did not, several other senators — including Johnson, Coats, Lindsey Graham of South Carolina and John Thune of South Dakota — joined in the criticism of Cruz.

"It just started a lynch mob," said a senator who was present.

Despite the uproar, Cruz did not offer a plan for how his party could prevail in the shutdown battle and suggested his colleagues were defeatists.

Republican elders worry that the tactics of Cruz and his allies in the House are reinforcing the party’s image as obstructionist, and benefiting Obama at a time when his standing with the public is sliding. A New York Times/CBS poll last week found that 49 percent of Americans disapprove of the president’s job performance.

"The story people see now is President Obama sinking like a rock for months, and the only thing holding him up are the Republicans," lamented Haley Barbour, the former governor of Mississippi who previously led the Republican National Committee. "We have to get to the best resolution we can under the Obama administration, and then focus on some other things."

The tensions reveal deeper divisions about how to address more fundamental problems facing the party. Nearly a year after a second consecutive and decisive presidential loss, the rebranding effort that almost every top Republican called crucial has been set aside or obscured by the wrangling with Obama.

That means there has been little progress on issues the party establishment believes are critical to a revival, like an immigration overhaul, or something conservative intellectuals are more eager for, like a populist-oriented economic approach.

"There are certainly opportunity costs to Republicans in the confrontations and crises we’re witnessing," said Pete Wehner, a former George W. Bush aide and a leading voice for change.

"Even if you don’t lay most of the blame on the GOP, there’s no question, I think, that the effort to reform and modernize the GOP — and to rally support among Republicans around that effort — is being at a minimum impeded."

And the spotlight on further dysfunction in Washington undercuts those Republicans who want to make less polarizing figures outside Washington — especially governors — the new face of the party.

"The fight here is important to have, this is an important part of political life," former Gov. Jeb Bush of Florida said at a recent news conference in the capital. "But I do think the emphasis of being against the president’s policies, no matter how principled they are, needs to be only half the story, if not less."

Bush cited the accomplishments of a three Republican governors and potential presidential candidates — Scott Walker of Wisconsin, Bobby Jindal of Louisiana and Chris Christie of New Jersey — who he said were offering "a more positive, hopeful, optimistic message."

Bush’s comments reflect what has become gospel among many Republican professionals: that the language and images projected by the Washington wing of the party are interfering with efforts to modernize.

In a speech this week to Republican state officials, Ed Gillespie, a former Republican chairman, lamented how members of the party’s congressional caucus were "always in the position of talking about what they’re against — what they want to block or repeal or defund."

"And we join them in staunch opposition to the president’s harmful policies — but our party might be better off if we spent more time speaking in positive terms about why we’re against those policies and, more importantly, what we’re for," said Gillespie, who is chairman of the group he spoke to, the Republican State Leadership Committee.

The constant focus on congressional and White House bickering especially annoys Republican governors who feel that the party can take back the White House in 2016 if they nominate one of their own and run not only against the Democrats, but also against Washington dysfunction, much as George W. Bush did in 2000.

"There’s a clear contrast there," Gov. Brian Sandoval of Nevada said of the difference between his fellow chief executives and Republicans in Washington. "People are craving leadership and craving problem-solvers."

Haslam of Tennessee noted that governors, unlike House members, have to answer to a much broader electorate, one where "the political pendulum swings back really fast."

"If you’re in a seat that’s 80 percent Republican, you don’t see the pendulum swinging by very fast," he said.