The debate over the fiscal cliff has turned the spotlight not just on the nation’s top CEOs but on the influential trade group that represents them, the Business Roundtable.

Having essentially sat out the recent elections, the Roundtable is mounting a six-figure lobbying campaign to warn Congress and the Obama administration about the perils of the automatic spending cuts and tax increases that will kick in if they don’t reach a deficit reduction deal. The campaign comes amid a hiring spree at the association, led by former Michigan Gov. John Engler, aimed at boosting the group’s Beltway profile.

The suddenly central role that Roundtable CEOs are playing in the debate has irked some business leaders representing small businesses, who complain that they are being shut out. But the Business Roundtable’s deliberately nonpartisan strategy — the group doesn’t even run a political action committee or score key votes — is turning out to be tailor-made for the fiscal cliff negotiations, which hinge on compromise. President Barack Obama is set to meet with congressional leaders Friday at the White House.

“We don’t score members of Congress; we don’t get involved in these big campaign expenditures,” said Roundtable Senior Vice President Bill Miller, who joined the group in June after a dozen years at the U.S. Chamber of Commerce. “And that gives these CEOs the opportunity to play in the middle. And I think that’s important.”

The Roundtable has spent $9.4 million on lobbying this year, according to the Center for Responsive Politics, ranking it second among Washington business associations, but still far behind the U.S. Chamber of Commerce, whose lobbying budget approached $96 million, according to the CRP. But Engler’s group is in the process of beefing up its lobbying, communications and policy shops. Miller is one of several high-profile new hires in recent months, including former Capitol Hill and GOP political aide Jessica Boulanger as vice president of communications, and more are on the way.

All 12 of the CEOs who met with Obama Wednesday at the White House are Roundtable members, half of them members of the group’s executive committee. They included the top executives of major companies including Aetna Inc., Dow Chemical Co., General Electric Co., and Procter & Gamble Co.

In the Roundtable’s “It’s Time to Act” campaign, which features web videos and print and radio ads, several of the CEOs warn that falling off the fiscal cliff would stall economic growth, boost unemployment and hurt the nation’s credit rating. Some, including Honeywell International Inc. Chairman and CEO David Cote, are also involved in the bipartisan Fix the Debt campaign, a $40 million organization that has launched its own ads urging Congress to act.

The role of the CEOs, who in some cases have suggested that a final deal may have to include tax increases, has sparked criticism from some quarters. Dan Danner, president and CEO of the National Federation of Independent Business, called Obama’s meeting with the executives “an insult to the business owners who create two-thirds of net new jobs.”

Danner said in a statement that “small-business owners are deeply disappointed that, once again, they are not at the table for discussions that will have a huge impact on their bottom lines and their ability to run and grow their businesses.”

Miller downplayed the friction, saying that “too much is being made of the differences between factions within the business community.” The Roundtable argues that lawmakers should enact a short-term deal to avoid automatic spending cuts and tax increases and raise the debt ceiling into 2013 so that Congress can debate tax and entitlement programs outside the lame-duck session.

Other business leaders have echoed that view. Even the U.S. Chamber of Commerce, which spent tens of millions on ads attacking Obama and other Democratic candidates in the recent elections, has avoided issuing ultimatums.

“We have not been proscriptive,” said Rob Nichols, president and CEO of the Financial Services Forum, which shares some members with the Roundtable. “We have not been drawing lines in the sand. We have been encouraging policymakers to come together in a bipartisan way to arrive at a deal.”

Overhauling the tax system and entitlements “needs to be developed in a thoughtful manner, and not under the gun in a lame-duck session,” said Dorothy Coleman, vice president of tax and domestic economic policy at the National Association of Manufacturers, where Engler served as president and CEO before joining the Roundtable in early 2011.

Engler, who was traveling and not available to comment, told The New York Times that “everything is on the table.” By contrast, GOP leaders on Capitol Hill, and leading anti-tax lobbyists, have rejected out of hand Obama’s plan to end Bush-era tax cuts for earners making $250,000 or more.

Despite tensions between the Obama White House and many CEOs during the presidential campaign, Engler has struck a deliberately conciliatory tone. On Election Day, he congratulated Obama.

“It isn’t about drawing lines in the sand,” Miller said. “It’s about drawing lines toward economic growth, the sooner the better. Because there is a lot of capital sitting on the sidelines waiting for Congress and the administration to come to some kind of agreement about taxes, the budget and entitlement reform.”