The question from the mayor of Minneapolis was direct and heartfelt, one big-city Democrat speaking to another: Would the leadership of the House of Representatives push for a "responsible" tax-increase to avoid spending cuts that could cripple the cities?

Rep. William H. Gray III, a liberal Democrat from Philadelphia and new chairman of the House Budget Committee, noted the results of the fall elections and said the political winds just weren't blowing in that direction.

A frustrated Mayor Jake M. Godbold of Jacksonville, Fla., then rose to offer a plea -- and a warning -- strong in language but typical of the sentiments of many of the 160 city executives who took part in the midwinter meeting of the U.S. Conference of Mayors that ended here yesterday.

"We in the cities are really beginning to see the effects of policies that went in four years ago. You guys in the Congress sit up there and say, 'Well . . . that's what the public wants,' " said Godbold, who then characterized the "what" with a barnyard epithet.

The mayors, he said, were on the front line, bearing the brunt of the unfulfilled promises of economic recovery. But, he lamented, "nobody listens to us."

The annual meeting here, largely ignored by the top ranks of a Republican administration preparing for inauguration, was dominated by calls for recognition and cries for help before the budget ax falls on many of the programs that the cities consider to be lifelines.

"I'm sure that writing this budget has been a painful task for the administration officials, and responding to it will be as painful a task for the Congress," the conference president, New Orleans Mayor Ernest (Dutch) Morial (D), said at the opening breakfast. "But for all of us, living with it will surely be the most painful task of all."

The cities have the distinction of having vital interests in at least three of the "six sob sisters of subsidy" identified by Office of Management and Budget Director David A. Stockman as prime targets for cuts: aid to state and local governments, small business subsidies and mass transit subsidies.

If President Reagan and Stockman prevail, general revenue sharing, urban development action grants (UDAG), the Economic Development Administration and the Small Business Administration would be eliminated, and there would be sharp cuts in federal housing subsidies and community development block grants.

At a time when mayors are complaining of sharp increases in the number of hungry, jobless, homeless and poor in their cities, there also would be cuts in federal welfare and health payments, child and family nutrition programs and energy assistance for the poor.

The Treasury Department has proposed eliminating the deductibility of state and local taxes and urged restrictions on some tax-exempt bonds used by cities to finance development projects.

About two-thirds of mayors in the conference who identify their political affiliations are Democrats. Most of Morial's public statements were peppered with phrases extolling the "bipartisan" concerns of the cities.

The conference's executive committee adopted two resolutions -- both linked to foreign affairs.

Boston Mayor Raymond L. Flynn sponsored one that said the organization would "encourage the direct removal of any public funds by the cities of America now invested in institutions doing business with South Africa."

Mayors Marion Barry of the District of Columbia and Thomas H. Cooke Jr. of East Orange, N.J., sponsored one that recommended aid for drought-stricken African countries in the form of food, "tools that will enable the people to feed, house and clothe themselves" and "funding for infrastructure development."