Mayors from the 10 cities with the nation's highest unemployment had high hopes when they came to Washington for help, but they are learning that it isn't so easy to move the bureaucracy.

The mayors, who range from George Vukovich of Youngstown, Ohio, where unemployment has topped 22 percent, to John Fedo of Duluth, Minn., over 20 percent, had demanded to see President Reagan. They settled for a session in January with Housing and Urban Development Secretary Samuel R. Pierce Jr.

Afterward, they told a news conference that their communities are in desperate straits, and that they hoped HUD would agree to set aside a percentage of federal grants and contracts for their unemployed.

In a recent response to Fedo, Pierce said he had checked the relevant statutes and found it would be illegal to earmark urban development action grants or community development block grants for particular cities.

Pierce said he would send economic development specialists to the 10 cities to help the mayors apply for UDAG projects.

The 10 petitioners were less than overjoyed. "The mayors generally felt the response was totally inadequate," said spokesman Dick Johnson.

ABOUT-FACE . . . . HUD has abruptly dropped a plan that critics say would have sharply restricted federal outlays for repairing public housing projects, and nearly everyone wants to take credit for the turnabout.

It began with a seemingly routine announcement on Feb. 9, when Federal Housing Commissioner Philip Abrams sent HUD field offices new instructions on how to spend $2.5 billion for public housing repairs. Abrams essentially lowered the standards so that most public housing units would be eligible only for minimal repairs. Lowest priority, he said, would be given to more expensive, structural improvements.

Congressmen and lobbyists for public housing, which shelters 3.5 million tenants, quickly mobilized. Robert Maffin, director of the National Association of Housing and Redevelopment Officials, said the plan would result in "minimal and superficial repairs." The group said HUD was all but writing off at least 90,000 rundown units.

Rep. Henry B. Gonzalez (D-Tex.), chairman of a House Banking subcommittee on housing, complained that the plan would "seriously undermine the basic intent of the program."

After 23 members of Congress sent a similar complaint, HUD rescinded the instructions March 16, making comprehensive repairs are again a high priority.

A HUD spokesman said that Pierce shelved the new regulations as soon as he learned of the matter, and that he acted mainly to create new jobs, not in response to congressional pressure. "I think Pierce deserves credit for moving succinctly on this thing," he said.