On a Monday last month, Rep. Greg Walden, chairman of the National Republican Congressional Committee, met with some top GOP donors for lunch at Le Cirque on Lexington Avenue in Manhattan. The donors, a youngish collection of financial industry types and lawyers, had some questions for Walden, a mild-mannered lawmaker from eastern Oregon known for speaking his mind.

Why, they asked, did the GOP seem so in the thrall of its most extremist wing? The donors, banker types who occupy the upper reaches of Wall Street’s towers, couldn’t understand why the Republican Party—their party—seemed close to threatening the nation with a government shutdown, never mind a default if the debt ceiling isn’t raised later this month.

“Listen,” Walden said, according to several people present. “We have to do this because of the Tea Party. If we don’t, these guys are going to get primaried and they are going to lose their primary.”

Walden asked how many of those seated around the table were precinct captains. These were money men, though, not the types to spend night after night knocking on doors and slipping palm cards into mailboxes.

“A lot of the people there didn’t even know what a precinct captain was,” said one attendee.

Not a single hand went up.

“I hear this complaint all the time,” Walden said. “But no one gets involved at the local level. The Tea Party gets involved at the local level.”

(An NRCC spokeswoman disputed that Walden mentioned the Tea Party at the event.)

It is unlikely that the gilded power brokers in the Republican Party are likely to join their local county political club any time soon, but as the stock market wobbles amid the government shutdown and the continued demand for an Obamacare delay, a number of GOP donors are wondering if it is time for a little outside counter-pressure to sap the Tea Party of some of its energy. To be clear, none are considering joining the Democrats, and they find plenty of fault with President Obama and Senate Majority Leader Harry Reid. The deficit, taxes, and regulation remain top concerns. But several top GOP donors say figuring out a way to “break the fever”—as Obama once put it—or at least keep their fellow party members from damaging the economy any further has become Topic A in their social set.

“We are finding a marvelous way to grab defeat from the jaws of victory,” said Fred Zeidman, a Houston-based businessman who was a major donor to both of George W. Bush’s presidential campaigns. “The way we are handling this has been a mistake from the beginning. I think we misread where the country was.”

Zeidman pointed to the way the Republicans handled Syria, which, he said, “allowed the administration to fall on their own sword.” He contrasted that with the negotiations around the budget, which he said have overshadowed what should be a winning issue for the GOP, Obamacare.

“The Tea Party is not looking at the big picture,” he said. “In the long run it will have deleterious effects on the whole party when we could have taken the high road. There is so much going on right now with Obamacare, and no one is saying a word about it.”

“I am not writing a check to anyone,” he added. “That is not working for the American people.”

Bobbie Kilberg, a Republican fundraiser who has worked for four Republican presidents, echoed Zeidman. She has hosted fundraisers for ideological warriors such as Reps. Paul Ryan and Eric Cantor, and is hosting Arkansas Senate candidate Tom Cotton later this year, but she said she will not give to the NRCC.

“When you have a small segment who dictate to the rest of the party, the result is what we have seen in the last two days,” she said. “People need to stand up and not be afraid of the Tea Party.”

“This may be a turning point,” she predicted. “People may say, ‘Enough already.’”

To be sure, there is still nothing like any kind of organized opposition to form a donor-class version of the Tea Party, one that mounts primary challenges to incumbents for being too unyielding. And if there were, the right wing of the GOP would still have deep pockets thanks to those conservatives who don’t work in the financial industry but, like the Koch Brothers, who are in the oil, gas and other industries, and who still see the problems of over-regulation as more serious than any kind of shutdown.

Some Republican operatives are dismissive of the donors’ concerns. The shutdown is still in the early days, and although it may look dire for Republicans, it is unclear what the future holds. The congressional map heading into the 2014 elections still favors the GOP.

“Obamacare continues to be our No. 1 fundraising tool,” said Andrea Bozek, communications director for the NRCC. “We have broken records in our online fundraising and engagement in the last few weeks. Thirteen months is a long time in American politics, and it’s going to seem even longer for House Democrats who will be spending that time defending Obamacare’s broken promises.”

Most of the Republican donors, fundraisers, and bundlers who spoke to The Daily Beast said they sympathized with House Speaker John Boehner, who is working under difficult circumstances. And some said they thought the whole notion of an-all powerful Tea Party controlling the agenda in Washington is a conspiracy bordering on the absurd.

“I have been in politics for 45 years,” said Georgette Mosbacher, a cosmetics CEO in New York whom The Washington Post once called “the eccentric grande dame of GOP fundraising.” “Every time something does not work, it has to be blamed on an entity ‘out there.’ Well, I am sorry, but the Tea Party isn’t that powerful, and anybody who stopped to think about it long enough would know that.”

But there is still a sense among the donor class that some countervailing force is needed to push back against the furthest edges of the party, regardless of what it is called.

“I have raised a lot of money, but I am not raising any more for House candidates,” said Munr Kazmir, a New Jersey-based businessman and major donor to George W. Bush. “I am angry. I am embarrassed to be a Republican sometimes, I tell you.”

Editors' Note: This post has been updated to clarify a statement from an NRCC spokeswoman.