The Fix the Debt campaign announced Thursday that 40 more corporate CEOs and business leaders had joined its cause. To some congressional denizens, that could translate into 40 more people with whom they are miffed.

Under the auspices of Fix the Debt and associations such as the Business Roundtable, CEOs flocked to Washington, D.C., last month for meetings with Obama administration officials and members of Congress urging a resolution to the fiscal cliff standoff.

By eventually blessing a deal that raised taxes on the country’s top income earners, the CEOs aggravated some congressional Republicans who had hoped any deal would include spending cuts, according to Capitol Hill and K Street sources.

As the executives plan their next rounds of meetings on both ends of Pennsylvania Avenue and more fiscal policy standoffs loom, some sources say the CEOs’ clout in typically friendly Republican offices may be waning. Leaders of the CEO-backed groups say the executives simply felt compelled to help jump-start lagging negotiations during which the U.S. economy hung in the balance.

“To a lot of Republicans, they’re deeply disappointed that the CEOs managed to position themselves as champions of tax increases,” one high-ranking GOP leadership aide said. “These are adults who didn’t seem to get the very obvious joke that the White House was using them as cover for tax increases while they had no real intention of cutting spending.”

This aide and other Hill colleagues, as well as numerous downtown sources, said many lawmakers and staffers believe the CEOs were cozying up to President Barack Obama in the hopes of positioning themselves well in a broader debate over tax reform.

Another Hill aide said the Obama administration manipulated the CEOs, who now may have lost some leverage in the coming debates. “Do we trust that they won’t get used again? Probably not,” the staffer said.

But former Michigan Gov. John Engler, who heads the Business Roundtable, pointed out that the CEOs of his organization supported the deal but did not broker it.

Republicans including Speaker John Boehner of Ohio and Senate Minority Leader Mitch McConnell of Kentucky did help craft it and urged their party’s support.

“None of our CEOs were able to cut any deals or for that matter weren’t asked to cut any deals,” Engler said. “We weren’t at the table.”

He said the CEOs felt compelled to make sure policymakers understood the gravity of the fiscal situation. Executives who weighed in during the fiscal cliff debate included Jeffrey Immelt, chairman and CEO of General Electric Co., Lloyd Blankfein, chairman and CEO of Goldman Sachs Group Inc., and Jamie Dimon, chairman and CEO of JPMorgan Chase & Co.

“The CEOs said, ‘These folks are pretty far apart, and there doesn’t seem to be a process,’” Engler said. “We felt as major employers … this was important to be resolved. Everybody cared so much and felt this was so important they were willing to put their name on the line. … They felt as citizens and business leaders in this country, you couldn’t be silent.”

Maya MacGuineas, president of the Committee for a Responsible Federal Budget and head of the Fix the Debt campaign, said her organization and the CEOs involved with it were “disappointed with the quality of the overall deal that members of Congress came up with to avoid the fiscal cliff.”

It didn’t touch entitlement spending or do enough to address the deficit, she said.

“I think the entire country was disappointed, and we would count the CEOs among those ranks,” MacGuineas added.

But, she said, the nation’s business leaders aren’t giving up. Not only did the group just sign on the 40 new executives, but she said she has just begun scheduling “a number of CEO fly-ins,” or lobbying visits. MacGuineas declined to say who, in or out of government, is planning on attending the sessions but said they will start in the coming weeks.

Fix the Debt will continue to push for a big deal on spending and debt, she added. “We’ve built up a very large organization with major resources to be used for something to fix the problem,” she said.

Members of Congress have criticized the business community in the wake of the bitter fiscal cliff standoff.

After the Senate approved its deal to avoid expiring tax breaks and automatic spending cuts, Sen. Bob Corker, R-Tenn., said on CNBC that voting for it, which he did, was like “eating a you-know-what sandwich.” He also issued a warning to business leaders.

“What I would say also to the business community is don’t be a lackey for the president like so many business leaders were this last go around,” Corker said in the interview.

House Ways and Means Chairman Dave Camp of Michigan issued a statement in December after reading a letter from more than 150 CEOs, distributed by the Business Roundtable, that warned of potentially grim economic consequences of going over the cliff and countenanced the possibility of increasing tax rates.

“Big business may support raising tax rates on small businesses, but I do not,” Camp said in his statement.

One Republican lobbyist who counts Fortune 500 companies among his clients said that some of the CEOs, “in my opinion, didn’t do themselves any favors, particularly with Republicans who tend to carry their water. I think a lot of them would have been better served to stay in the background.”

This lobbyist said staffers on Capitol Hill have made sure to register the displeasure of themselves and their bosses.

On the flip side, though, the business leaders had an obligation to their shareholders, and they were gravely concerned about the consequences of going over the fiscal cliff.

Michael Needham, who runs Heritage Action for America, said the CEOs were just looking out for their corporate bottom lines.

“To be a CEO in America today … you’ve got to know how to play the Washington game,” he said. “There are a lot of businesses that are trying to use what’s going on in Washington to advance their business interests, and good for them. That’s what they’re supposed to do.”

Engler said his CEOs continue to advocate for entitlement and tax reforms, among numerous other issues. When it comes to concrete fiscal ideas, Engler said, the CEOs have been impressed with Camp, Corker and Sens. Lamar Alexander, R-Tenn., and Max Baucus, D-Mont., among others, who have specific proposals.