Anyone watching the Washington budget debate over the past decade must have wondered why there didn’t seem to be any grown-ups in the room — someone who could cut through what Honeywell’s Dave Cote calls the “hysteria, histrionics and hyperbole” and force the bickering children to agree on a reasonable compromise.

That’s what the voters want, what the economy demands and what country must now have to regain its confidence and its global influence.

Some grown-ups who have been noticeably absent from this conversation have been the heads of the country’s major corporations, who talk a good game about deficit reduction but haven’t invested the time, money and political capital necessary to jolt the political system from its dysfunctional equilibrium.

That’s about to change. Last week, the first battalion of CEOs showed up in Washington, reporting for duty.

It all started last year when corporate executives looked on in horror as the ideological tong war in Washington nearly led the country to default on its debt. As the crisis was developing, they assumed it was just the kind of posturing that characterizes any high-stakes negotiation.

By the time they realized it wasn’t innocuous brinksmanship and began to engage, it was too late.

Although default was narrowly avoided, the damage to the markets and the economy was real. And subsequent events — the breakdown of the Obama-Boehner talks on a grand bargain, the failure of the congressional super-committee — have convinced a number of CEOs that they had to get involved, particularly with a fiscal cliff looming in January.

During the past year, there have been quiet meetings put together by chief executives such as Cote, Aetna’s Mark Bertolini and JPMorgan’s Jamie Dimon, and Senators Mark Warner (D) and Saxby Chambliss (R), the ringleaders of the bipartisan Gang of Six. Nudging it along and pulling it all together has been Maya MacGuineas, who for a decade has been sounding the deficit alarm from the Committee for a Responsible Federal Budget.

Last week, the group, calling itself Fix the Debt, went public at a news conference urging the president and Congress to embrace a deficit-reduction plan along the lines suggested by the bipartisan Simpson-Bowles Commission, which included reforms of a tax code that produces too little and entitlement programs that spend too much.

“Think of it as Simpson-Bowles 3.0,” said former Republican senator Judd Gregg of New Hampshire, who is co-chairman of the effort along with Ed Rendell, the former Democratic governor of Pennsylvania.

In addition to Cote, Dimon and Bertolini, the charter business members include Sandy Cutler of Eaton, Gregg Sherrill of Tenneco, Marty Flanagan of Invesco, Gary Loveman of Caesars, Thomas Quinlan of R.R. Donnelley & Sons and financiers Steven Rattner and Pete Peterson.

Later that evening, at Honeywell’s Washington office, over a salmon dinner with the floodlit Capitol dome as a backdrop, the executives huddled with their political co-conspirators: Simpson and Bowles, Warner and Saxby, and Rep. Steny Hoyer, the No. 2 Democrat in the House. Also on board: Simpson-Bowles commissioners Dick Durbin, the No. 2 Democrat in the Senate, and Andy Stern, former president of the Service Employees International Union.

In the next two months, the group aims to raise $50 million to $100 million, mostly from big corporations, to build public support for a debt deal and flush out its details so it can be acted on by Congress sometime after the November elections.

In many ways, this CEO effort is an end run around the elaborate and expensive apparatus that big businesses have set to influence the government in Washington, whether it be Washington offices staffed by company lobbyists or myriad business and industry associations to which they pay significant dues.

In today’s highly partisan and polarized environment, the only way these business lobbyists can shape legislation or regulations of interest to their industry is to ally themselves with one party or the other and back that choice with a steady flow of political money to the party, its leaders and affiliated political-action entities. The natural choice for business has been the Republican Party.

The problem for Corporate America, however, is that the same Republicans who have been so aggressive and uncompromising in pursuing their agenda on energy or trade or corporate taxes turn out to be no less aggressive and uncompromising on issues that business may not agree on, such as eliminating federal funding for education, denying the existence of global warming or destroying Planned Parenthood.

Most significantly, while the vast majority of corporate executives would jump at signing on to a long-term budget plan that combines entitlement cuts with increased revenue, the Republican caucuses in both houses have repeatedly refused even to consider such a compromise. So does the Republican presidential candidate.

What would happen if a major company or industry group business organization were to break with the Republican caucuses and lobby for a bipartisan budget compromise? For starters, they might suddenly find that that amendment they were counting on won’t be coming up for a vote after all. And if they persist in such disloyalty, the company lobbyist or top official in such an industry group might discover that there is a quiet effort to get them fired, replaced with somebody more loyal and reliable.

Crazy conspiracy theory? No, it’s actually called the K Street Project, begun a decade ago by House Republican Leader Tom Delay. And if you doubt its effectiveness, just ask former Republican Congressman Billy Tauzin, who was pushed out as head of the Pharmaceutical Research and Manufacturers of America because he dared to strike a compromise deal with the Obama White House on health-care reform.

The reality now facing practical, pragmatic corporate executives is that their Washington lobbying apparatus has become one with a Republican caucus on Capitol Hill that is dominated by ideological zealots and uncompromising partisans. So if they have now concluded that the most important issue for American business, and the economy, is getting a reasonable bipartisan compromise on taxes and spending, their only choice is to bypass that apparatus.

Just for fun, go to the Web site of the U.S. Chamber of Commerce, which has become nothing more than a political money-laundering operation for the Republican Party. There you will find an endless stream of hysteria, histrionics and hyperbole demonizing Obama and warning of economic Armageddon if taxes are raised. And yet this is the same Chamber of Commerce that gets much of its income from the same corporations whose chief executives now consider a budget compromise involving higher taxes as their top priority.

(A similar dysfunction, by the way, exists on the other side, where labor unions and the AARP have joined with the leadership and Democratic caucuses in Congress to squash any talk of cuts to Social Security, Medicare and Medicaid as part of a budget deal. When John Rother, the longtime policy director of the AARP had the nerve to declare that some cuts were inevitable, it wasn’t long before he was working somewhere else.)

So it’s great that dozens of the nation’s top business leaders have decided to join this fight and put some serious money behind it. They shouldn’t waste their resources, however, trying to “educate” the public about the need to tame the deficit. For one thing, the country already gets it. For another, any advertisements they might run will get lost in the $2 billion tsunami of negative campaign ads that are about to break over an already cynical electorate.

To pull this off, my back-of-the-envelope calculation is that Fix the Debt will need to raise $278 million. That may sound like a lot of money, but it works out to one-third of one percent of the profits earned last year by the Fortune 500. More significantly, its enough to provide $1 million in political air cover in the next election to each of the 60 senators and 218 House members, Republican or Democrat, who have the courage to vote for a bipartisan budget compromise next year. And by the time the tea party, Grover Norquist and the AARP are finished with them, most of them will need it.

Even at $278 million, however, a credible budget deal would still provide the captains of industry a Bain Capital-like return on investment. The boost it would give to the economy and the financial markets would far exceed any stimulus proposed by either party or either of the presidential candidates.

As Robert Zoellick put it last week, quoting Australia’s foreign minister: “The U.S. is one budget deal away from restoring its global pre-eminence.”