Fed-up leaders are mounting a counterattack against other Republicans sniping at their party’s presidential nominee, Donald Trump, saying the GOP should fire anyone caught bad-mouthing the ticket.

Oregon Republican Chairman Bill Currier will ask his state party’s central committee to formally petition Republican National Committee Chairman Reince Priebus to discipline party staff, consultants or vendors who speak or work against their candidate.

“Trump won the nomination in fair competition, and now that he is the nominee, the RNC should support him, including those we hire at every level,” said Mr. Currier. “If we don’t do that, we have strayed from our mission.”

He said some response is needed after a surge of reports of discontent within the Trump campaign and the broader Republican Party as Mr. Trump’s poll numbers tumble.

Despite a stunningly good July for fundraising, in which Mr. Trump collected more than $80 million for his campaign and associated party committees, the press — chiefly citing unidentified sources — has said the campaign is in free fall.

“ABC News has learned that senior party officials are so frustrated — and confused — by Donald Trump’s erratic behavior that they are exploring how to replace him on the ballot if he drops out,” that network’s Jonathan Karl reported on Aug. 3.

A Washington Post story, again citing unidentified sources, reported that Mr. Priebus was “very frustrated” with the Trump campaign and had “run out of excuses to make on the nominee’s behalf to donors and other party leaders.”

The anonymous drip-drip-drip of negative comments will take its toll eventually, said Oregon RNC member Solomon Yue, who is co-sponsoring Mr. Currier’s resolution calling on Mr. Priebus to pink-slip renegade employees.

Neither man was a supporter of Mr. Trump’s at the beginning of the campaign, but both said they have had it with the carping.

“When Mitt Romney in 2012 made his self-deportation comment about illegal immigrants, I didn’t see pro-amnesty senators like Lindsey Graham and John McCain pile on.

“And when Hillary Clinton lied about what FBI Director Jim Comey said about her, I didn’t see any Democratic senators pile on her either,” said Mr. Yue. “So whey are we so eager to destroy one of our own?”

The Republican Party’s war with its own consultants began nearly four years ago, after presidential nominee Mitt Romney lost an election that analysts had said was winnable. In its postelection analysis, the party said some consultants appeared to be more interested in their own bottom lines than in helping their party win, and recommended reining in what the party called the “consultant class.”

Mr. Trump’s campaign style — centralizing decisions with himself and close family members — appeared to have broken the consultants’ hold. But as he has slumped in the polls, the consultants are firing back, saying the nominee needs a firmer leash.

Rhode Island Republican Party Chairman Brandon Bell said the national committee’s staff and consultants should be required to show allegiance to their ticket because it’s the best way to enforce the kind of unity a party needs if it is to operate effectively.

“I think in particular, people who work for member services and opposition research are the ones who have to be for the nominee,” said Mr. Bell.

But Pennsylvania Republican Party member Robert Asher said a blanket rule may not work.

“I would think Reince and his folks expect staff and employees to support the ticket,” said Mr. Asher. “But if some didn’t, I would want to know the circumstances and facts before I would judge.”

The RNC’s rule book already imposes a loyalty requirement on its 168 members. Rule 4b states: “The Republican National Committee shall have the power to declare vacant the seat of any member who refuses to support the Republican nominee for President of the United States or Vice President of the United States.”

Republicans said it’s difficult to think about enforcing that rule.

“It’s a steeper hill to eject members elected by their state parties’ central committees than to fire staff or outside contractors,” said Mr. Currier. “It would take something egregious to bring the whole national committee to eject a member.”

Others, though, said firing people would make things even tougher for the campaign.

“How are you going to find experienced, loyal replacements for experienced, disloyal staff and consultants only 80 days before the election?” said Mike Karem, a former Republican Party operative who has worked in every presidential campaign from Richard Nixon’s to George W. Bush’s.

But the price of unity may be worth it, said former Reagan White House aide Mary Ann Meloy.

“The RNC has the right and responsibility to require the loyalty and support of all employees for the candidates of the Republican Party,” she said. “Otherwise, the RNC would be failing in their responsibility and duty to the registered members of the Republican Party who have chosen the candidates.”

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