US mayors are wary of 'new federalism'. Many applaud Reagan goals, but are concerned about impact of dismantling social programs

''New federalism'' may be a catchy phrase, but many of the nation's mayors are not pleased with the way it is working out in practice. They want to redefine it while there is still time.

While applauding President Reagan's general goals of less government, greater efficiency, and more private initiative, many say they have been handed major new responsibilities with virtually no money to back them up.

The mayors say that cities and social services have had to bear more than their fair share of the budget cuts. And the mayors will get the lion's share of the blame from citizens who are not protected by the Reagan administration's ''safety net.''

What emerges from debates on the issue at both the National League of Cities (NLC) meeting here in Detroit this week and a special session of the US Conference of Mayors in Chicago a few weeks ago is a yellow caution signal for the administration.

Many of the nation's big-city mayors from both political parties are urging Washington to go slower and take a more careful look at which level of government ought to be responsible for which services.

Most of them insist that the federal responsibility goes well beyond national defense. Some, like Mayor Vincent Schoemehl Jr. of St. Louis, a city which is 47 percent black and has lost much of its wealthier population to the suburbs, suggest that as a democracy, this country has cherished decent housing, education, feeding the poor, and provision of at least minimal health care as national priorities since the days of the depression.

''You can't lay these responsibilities on the older cities of this country like Chicago, St. Louis, and Cleveland and expect them to supply the resources for it,'' Mr. Schoemehl says. ''We don't have the tax base. The question is whether the cost is going to fall on those not able to pay.

''New federalism is the choice between progressive and regressive government, '' he says. ''The wealth of this country has to be redistributed, or we have to abandon our goals.''

Mayor Edward I. Koch of New York City, in a major address at the NLC meeting, similarly described new federalism as a ''mask . . . for a systematic campaign of abandonment'' of the nation's cities and their special needs. ''It is a sham and a shame,'' he said, in a country which aspires to be a ''land of equal opportunity.''

''The administration knows that the states and localities can't assume the cost of both lifting the poor and rebuilding the infrastructure,'' says Mr. Koch. ''The numbers just don't work out on a local level.''

Both mayors are Democrats and their comments could easily be dismissed as strictly partisan. But the views of leading Republicans at the NLC conference, though more gently phrased and coupled with more kudos for the President, were equally intent on the need for a change of course by the Reagan administration.

Republican Mayor George Voinovich of Cleveland, for instance, says that Washington's current failure to pay closer attention to the short-term social impact of the budget cuts and the transfer of authority from the federal level to the local could prove to be the ''Achilles' heel'' of the new federalism.

Mr. Voinovich says it is unrealistic to try to dismantle in three to four years what has developed over four decades. He counts it a similar mistake for the President to insist on an across-the-board cut.

''If you're going to cut programs, it should be done with a scalpel, and not a meat ax.''

Vermont Gov. Richard Snelling, chairman of the National Governors' Association and a man who precedes his remarks these days by saying he is a conservative Republican, suggests a moratorium of one or two years on all further budget cuts. He urges a joint state-city effort to draft a federalist plan that would be neither a ''return to the old grant-in-aid grab bag of the ' 70s or an abdication of clear federal responsibility.''

He also suggests developing a calendar for action that would protect those most affected by the budget cuts. And Gov. Snelling has urged city leaders to join in the call for a domestic summit to get their views across to the Reagan administration.

''I don't think anything said in Washington so far is cast in concrete,'' he says. ''And I think the next 30 days are critical.''

In the shift of powers under way, many cities have been concerned that the newly powerful states may put them in the position, as Indianapolis Mayor William Hudnut puts it, of being ''the neglected little brother.''

Both Governor Snelling and Mayor Hudnut, a Republican and president of the NLC until the end of the conference here, reason that focusing now on the common problems that unite cities and states would serve both the best.

Though Mayor Hudnut says states could afford to be more generous to cities in granting them broader legislative and taxing powers, he agrees on the need for a united front in Washington. ''We're all in the same boat and it can't sink at one end,'' he says.

Officials in both cities and states are busily discussing what President Reagan meant when he promised to turn revenue as well as power back to lesser government levels. So far, city leaders contend, all they have seen is the three-year federal tax cut.

There has been some talk, but never by the President, of turning a specific federal tax, such as that on liquor or cigarettes, back to the cities. What most city leaders would prefer is a lump sum with few strings, such as they now get with revenue sharing.

Those attending the NLC conference say they are distressed about rumors from Washington that Budget Director David Stockman is preparing to phase out new spending after 1983 in Community Development Block Grants and Urban Development Action Grants.