In this publicity-saturated city, where there seem to be more microphones than manhole covers, Mayor Edward I. Koch may be the biggest one-man publicity machine in town. Although he lost much of his political leverage in state and national politics when he was beaten by Gov. Mario Cuomo in last year's Democratic gubernatorial primary, Koch has not lost his voice.

In recent weeks, he has raised it in a warning to his party about reverting to what he has called "the follies of the McGovern-Carter era," and especially about "catering to special interests." "Our presidential candidates are not extremists," he told me in an interview last week, "but they're walking down that McGovern path of pandering to the most extreme elements of every constituency on every issue."

Koch's warning will be echoed by many other politicians and pundits this week, as the National Education Association and the AFL-CIO deliver their endorsements of a Democratic presidential candidate and almost all the aspirants bid for the support of the National Organization for Women.

What Koch said in a speech to San Francisco's Commonwealth Club last month is going to be heard in many variations: "Catering to special interests has the potential to do more harm than good."

As the candidate favored to win the backing of the NEA and the AFL-CIO, Walter F. Mondale is most vulnerable to the "pandering" charge. A top strategist in his campaign said last week, "These endorsements can hurt him if he seems to be buying in on the terms the endorsers have set. They help him if these groups seem to be accepting him as the leader of the Democratic Party's traditional coalition. That's why it's important that he get out front of this question and define his candidacy in those broad terms."

The best chance Mondale has for that will be when he goes before the AFL-CIO convention next week to accept its all-but-certain support. That speech could be the most important so far in his campaign. But the question of special-interest influence is not going to be dismissed by one oration. It will be around for the Democrats and--in ways not often noted--for President Reagan as well.

What is a special interest? Koch in his San Francisco speech and in the interview focused criticism on minority groups and activist women who demand quotas or preferential treatment as a remedy for the special-interest category.

Those definitions seem tailored to his own New York City political strategy of not very subtly playing off middle-class whites against blacks. Equally parochial was the letter he sent off to the presidential candidates asking their positions on two issues: a federal takeover of state and local Medicaid and welfare costs and U.S. policy toward Israeli settlements on the West Bank.

The notion that these might be "special-interest" concerns for a mayor of New York really had not occurred to him, Koch said, with all innocence.

Koch's speeches and statements on this subject have drawn mixed reviews from other Democrats but have been praised by people like William F. Buckley Jr., who, generally speaking, are not out to help the Democrats. Clearly the Republicans think they have a good issue in labeling the Democrats as captives of special-interest groups.

But a couple of issues last week showed that President Reagan is not exempt from similar pressures himself.

When Charles Lichenstein, a conservative ideologue from the Barry Goldwater era, now serving on the U.S. delegation to the United Nations, suggested that many Americans would be happy to see the United Nations pack up and move, Reagan was quick to agree. This was a tip of his hat to the anti-U.N. sentiments of the old isolationist wing of the GOP.

But as president, he knows better, so he swiftly turned around and said all the normal, reassuring things to the U.N. about U.S. adherence to the principles of the world organizations, and started lobbying against a cutback in U.S. funds for its support.

An even more painful dilemma was presented by the latest offensive statement from Secretary of Interior James Watt. Watt has been the living symbol of Reagan's political due bill to the right- wingers of the mountain states and their allies in the oil, gas and mining industries, operating through Sen. Paul Laxalt of Nevada and campaign contributor Joseph Coors.

Even when many of the Republicans on Capitol Hill and most of his in-house political advisers were telling him that Watt had become an unendurable political burden, Reagan hesitated to break his commitment to the special-interest constituency that picked Watt in the first place.

This special-interest game cuts both ways.