Faint glimmers are appearing that Republican grown-ups have decided to reclaim the schoolyard, but there’s a long way to go for the party to avoid long-term disaster.

Even Speaker John A. Boehner’s defiant-sounding statements Sunday demanding concessions from President Barack Obama can be interpreted as an appeal for face-saving help from the president, giving him permission to rely on Democratic votes to reopen the government and temporarily lift the U.S. debt ceiling to avoid a catastrophic default on the national debt.

Reportedly, other grown-ups — House Ways and Means Chairman Dave Camp, R-Mich., and Budget Chairman Paul D. Ryan, R-Wis. — are working on a GOP negotiating position that might lead to a “grand bargain” with President Barack Obama on entitlement and tax reform.

Another good sign is that Senate Republicans, conservative activist Grover Norquist and the Wall Street Journal editorial page are criticizing Sen. Ted Cruz, R-Texas, for causing the party to get major blame for closing down the federal government.

Journal columnist Kimberley Strassel last week exposed the hard-line Senate Conservatives Fund and Heritage Action for America’s Jim DeMint for attacking less-extreme Republicans as a means of raising money, not helping the party.

But such moves — and warnings issued by GOP gurus such as Karl Rove, former Florida Gov. Jeb Bush and Louisiana Gov. Bobby Jindal — are only the beginning of what it will take to save the GOP from being what one grown-up calls “a reactionary congressional party” that can’t win national elections.

What it will take is for the grown-ups to stop allowing the tea party and its allied jihadists to dominate the party’s policy and image — and then develop a positive agenda for appealing to constituencies outside the GOP base.

It was the tea party minority of the House Republican Conference — egged on by Cruz — that forced Boehner to abandon his original plan to avoid a government shutdown by passing a continuing resolution that didn’t demand “defunding” of Obamacare.

Even though grown-ups in the party argued that the Cruz/tea party defunding strategy was doomed and foolish, Boehner went along to avoid having to rely on Democratic votes — and, possibly, a right-wing effort to topple him.

However, it’s clear there’s no satisfying the tea party/Cruz/DeMint/Club for Growth/Freedom Works cabal. Any deviation from their purist line opens a Republican to attack as a “Republican In Name Only” and a possible primary election challenge.

Even Senate GOP leader Mitch McConnell of Kentucky and House Rules Chairman Pete Sessions of Texas aren’t immune to primary challenges, along with sometime-moderates such as Sens. Lamar Alexander of Tennessee and Lindsey Graham of South Carolina.

According to a new Gallup poll, national support for the tea party is near its record low — 22 percent —and its support among Republicans has dropped from 65 percent in 2010 to 38 percent now.

Only 46 out of 232 House Republicans and five of 46 senators officially belong to the Tea Party Caucus. GOP senators have shown some gumption in resisting Cruz’s tactics. But House Republicans haven’t; that’s because of what amounts to political terror tactics — the threat of a primary from the right.

The tea party is becoming for the GOP what Salafists are to Islam — practitioners of takfir, the right to expel (even murder) fellow believers deemed apostate.

As the 2012 election results, subsequent polling and various party critiques demonstrate, the GOP is in serious need of rebranding to appeal to groups outside of its South and Mountain West base of white males, evangelicals and senior citizens.

That’s especially the case with Latinos and younger voters. Rove has counseled that the GOP can’t win the presidency unless it carries 40 percent of the Latino vote (versus Mitt Romney’s 27 percent). Romney actually defeated Obama among Americans over age 30 but lost 18- to 29-year-olds (and the election) by 5 million votes.

A must-read survey by the College Republican National Committee found that when “winnable” young Obama voters were asked what words best describe the GOP, “the responses were brutal: ‘closed-minded,’ ‘racist,’ ‘rigid,’ ‘old-fashioned.’”

Yet the tea party and its organizational and media allies are on their way to defining the GOP brand — and institutionalizing just those impressions about the party.

Their immigration policies and restrictive voter-identification laws look distinctly anti-minority, and their opposition to same-sex marriage, emphasis on fiscal austerity and the absence of a job-creating economic agenda turn off young people.

To save itself, the GOP immediately has to get out of the hole it’s dug for itself by reopening the government and avoiding a debt default, then advancing a reasonable long-term debt package. Boehner and House Republicans have steadily backed off from their original stance of demanding defunding of Obamacare. Obama should call Boehner and see what it will take to facilitate a full retreat.

Then, the GOP has to adopt policies on immigration and growth that will give hope to demographic groups that will define America’s future.

But it can’t do any of this under a perpetual threat of reprisal from the tea party and its allies, which must be reduced politically to the noisy rump that they really are.

It will take courage on the part of grown-ups — in the first instance, Boehner, who may have to risk his speakership.

But it will also take organizational effort — and money — from groups such as the U.S. Chamber of Commerce and the Business Roundtable to defend reasonable Republicans against extremists. The Washington Post reported Monday on a few such moves. There have to be a lot more.

Presumably, Republicans would like to see one of their number in the White House some day. But the way things are going now, they never will.