In Peter G. Peterson's view, the 500 business leaders and educators who have endorsed the well-publicized "bipartisan appeal" for federal budget cuts are speaking for "a new silent majority."

If Peterson, one-time White House aide and Commerce secretary in the Nixon administration, is right, the 1980s' version of the silent majority consists of taxpayers worried about the escalating costs of government payments to a broad spectrum of the population. And if a pro-business coalition is forming that shares his concern about the impact of federal entitlement programs on the budget, it could become a political force in the coming years.

For now, however, it's hard to tell. When the going gets tough politically, business leaders, particularly those on Wall Street, often run for cover. But Peterson, now chairman of Wall Street's Lehman Brothers Kuhn Loeb Inc., said in a recent conversation that he hopes the Bi-partisan Budget Appeal coalition put together last year is more than just a one-shot media blitz.

His economic concerns center on ballooning federal budget deficits. The business group's appeal to Congress and the administration is to cut the 1985 federal deficit by $175 billion through a combination of defense spending reductions, freezes on pension and Social Security indexing, a favorite Peterson principle, and tax increases. His broad political concerns extend beyond that immediate goal, however.

Rarely, if ever, have so many influential members of the private sector made so blunt a political appeal as the two-week-old advertisement warning of the current federal "budget disaster."

While the ad was conceived and composed primarily by Peterson, the recruitment of the signatories was mostly a group effort involving five former Treasury secretaries from both major political parties. So far, the group has no staff to speak of, although some recruiting seems to be in the works, if Peterson's fund raising succeeds. Peterson says he pulls himself out of bed at 5 a.m. every morning to sign the organization's correspondence. "The word processors are just wonderful," he says.

Throw in a little merchandising help from the Washington public relations firm Gray & Co.--which helped garner recent slots for the group's leaders on each of the major television networks--and a media event suddenly becomes a potential political force. By recruiting private-sector big shots from both political parties, Peterson can keep his activities from taking on a political color, and by focusing on the 1985 budget, he also puts himself in a position to ignore the partisan political battles over President Reagan's current budget for 1984.

That allows Peterson to sound more philosophical than political in talking about what sounds like the beginnings of a political movement. "There's a huge silent majority of people like me that has worked real hard and paid their taxes and are concerned about their job and their family and so forth," he says. "The politics of the entitlements issue is built around the recipients. There is a big coalition for consumption, but very little for investment.

"The recipient groups at the end of the vending machine are beautifully organized. The Gray Panthers, the AARP American Association of Retired Persons , the military pensioners are in there wonderfully organized and the rest of the country, which I now call the 'new silent majority,' are never heard from.

"It's that asymmetry that's really the problem here," Peterson argues. "These organizations, their whole lives are devoted to perpetuating these systems and seeing that nothing happens to them. If we wait 10, 20, 30 years and there are two or three times more elderly, then the problem gets more complicated. There is potential here for some fairly significant problems."

Republican businessman William Simon, the former Treasury secretary, also believes the group is unlikely to fade into the political woodwork. "There were certain people in the White House trying to get us to cease and desist," he says wryly. "We're staying away from partisan politics and that astonished everybody in the White House. We're private citizens and we've offered them all the help we could give them and we've made an impact."

Meanwhile, Peterson's word processor is continuing to crank out correspondence. He's trying to interest, for example, women's groups, minority groups and youth groups in the cause, while preparing for congressional testimony at the same time. "I think it's a tragedy that the youth of this country are going to have to pay for these programs and are not really involved in the process," Peterson says.

None of this is to suggest that there's a grand scheme afoot here to develop a political base for Peterson or for any other candidate or party, for that matter. Peterson is amiable, self-effacing and experienced but seems to want little out of the whole operation for himself.

But there might be untapped political strength available for someone like Peterson. His group's success at bringing attention to their view of the world shows that even in the era of giant political action funds, with just a bit of cash, a telephone, a word processor and publicity hype, it's easy to mobilize worried business leaders in a troubled economy.