Conservative groups that led the charge during the October fiscal fights plan to sit out the high-profile confirmation debate over Janet L. Yellen to chair the Federal Reserve.

Republican senators are already promising sharp opposition to Yellen, whose confirmation hearing Thursday will be punctuated by GOP grievances on monetary and regulatory policies, and some lawmakers have threatened procedural holds to her nomination. But it looks like Republicans may be able to vote for her without tarnishing their records with top conservative groups, helping to ensure she’ll have the 60 votes needed to overcome a filibuster.

The Club for Growth and Heritage Action for America, two prominent organizations that have not shied away from battles with the pro-business wing of the Republican party, appear ready to spend the Yellen fight on the sidelines.

“There’s no mystery and it’s not complicated. We just almost never take a position on monetary policy,” said Club for Growth spokesman Barney Keller in an email. “Thus, we probably won’t be involved in the Yellen nomination.”

Don’t expect much from Heritage Action, either, said the group’s spokesman Dan Holler.

Although tea party activists in general loathe the Fed and what they deride as the central bank’s “loose money” policies, the apparent lack of a full-fledged campaign against Yellen suggests a reluctance to launch an effort that would rattle markets. The Senate Banking Committee hearing, and debates on her confirmation, come only a couple of weeks after the battle over the government shutdown and raising the debt ceiling, a fight that displayed fissures within the GOP over strategy and a gap between hard-line conservatives and traditional, pro-business Republicans.

Tea party activists and the elected officials they support have blasted the Fed for its policies on low interest rates, bond-buying and financial regulation, but GOP senators have not mounted a serious threat to Yellen’s confirmation.

One of her chief critics — Sen. Rand Paul, R-Ky. — concedes that she is likely a shoo-in for the central bank’s top slot, never mind the political polarized response to Fed policies since the 2008 financial collapse; Chairman Ben S. Bernanke, whose term expires Jan. 31, received 30 “no” votes — the most ever for a Fed chair nominee when he was advanced for a second term.

But no nominee to lead the Fed has ever been filibustered or rejected by the Senate. Such a scenario might roil financial markets.

In the division over the Fed within the Republican Party between Wall Street supporters and the populist tea party, in this case, the business side seems to be winning.

Just off the bruising debates over the nation’s debt ceiling and the government shutdown, few crave a war that could put financial markets in turmoil, said Greg Valliere, chief political strategist with the political intelligence firm Potomac Research Group.

“So many people feel a bit chastened by putting the country through such a debacle with the shutdown and debt limit that I think this inclination to go for brinkmanship has diminished since October,” Valliere said.

Averting Scorched Earth

Yellen, a Democrat who currently serves as the Fed’s vice chairwoman, has strong backing on Wall Street. The Fed’s monetary stimulus program intended to curb unemployment, which Yellen championed, has also helped fuel big gains in the financial sector.

Many of the Fed’s detractors say the quantitative easing, with its $85-billion-a-month buying spree in Treasury and mortgage-backed securities has helped Wall Street, but not Main Street.

“I understand that some of the tea party types have antipathy toward Wall Street. I get that,” Valliere said. “But at the same time, there’s an aversion to upsetting the markets. There’s an aversion to more scorched earth.”

Mark Calabria, director of financial regulation studies at the Cato Institute and a former GOP aide on the Senate Banking Committee, said the advocacy groups may have decided another battle wasn’t worth it, particularly without solid GOP unity.

“Republicans have basically pre-emptively caved,” Calabria said. “I think there is a sense that it’s a fight that’s already been lost.”

He noted Yellen would be the first woman to head the central bank, a historic occasion that could influence GOP votes.

“I’m not going to say the gender of Janet Yellen is going to determine how Sen. [Susan] Collins is going to vote, but I think it’s a factor,” Calabria said of the Maine Republican.

The decision of conservative groups not to key-vote Yellen’s nomination would avoid stirring up further internecine battles in a Republican party wrestling with its stances on major policy questions.

“They’re in a unique spot where they’re trying to repair relationships with the Republican caucus, and I actually believe that’s a factor here,” Calabria said.

With the biggest players in the conservative movement so far not engaged, that has left smaller organizations, such as American Principles in Action, to take the lead in mobilizing opposition to Yellen.

“It’s just a huge void within the conservative policy movement,” said Rich Danker, the APA’s economics project director. “If you’re an organization like Heritage for limited government, wouldn’t you want to weigh in on the fact that the Fed has been running a policy initiative to buy government debt? It boggles my mind.”

It’s also a sharp contrast to a recent fight over another financial regulatory nomination — that of Rep. Melvin Watt, D-N.C., to take the helm of the Federal Housing Finance Agency.

Republicans filibustered his nomination, with the help of the Club for Growth and Heritage Action, which included Watt’s cloture vote on their annual “key vote” score cards.

FreedomWorks, another conservative group, supports Paul’s legislation to “audit” the Fed’s monetary policy and wants to see a vote on that in concert with Yellen’s nomination.

“Our concern is more with the institution itself rather than who’s running it,” said FreedomWorks’ chief economist Wayne Brough.

Salim Furth, an economist with the Heritage Foundation, which is affiliated with Heritage Action, said he is skeptical of quantitative easing and other Fed policies, but that inside his organization economists take different views.

The Fed, he said, is “reinventing monetary policy. Clearly, there’s a lot we don’t know about what’s being tried now.”

Ben Weyl contributed to this report.