Leaders of Philadelphia's AFL-CIO unions have voted for a one-day general strike against the city Oct. 28--an action that could become an interesting footnote in U.S. labor history or an acute political embarrassment to the city's labor movement.

General strikes are across-the-board shutdowns of a citizenry's public and private services. They rarely occur in this country at any governmental level.

But Wednesday night the Philadelphia Council of the AFL-CIO unanimously voted for such a walkout in support of nearly 22,000 public school teachers and other employes who have been on strike since Sept. 8.

"I don't think there was any recourse to calling the general strike," Ed Toohey, president of the Philadelphia federation, told The Washington Post yesterday.

"The teachers' union president John Murray asked our members for their support and they gave him a 100 percent endorsement. There was no backing off," said Toohey, who conceded that he personally would prefer "not to have to do this."

In the federation's traditional spirit of union autonomy, each of the city's 350 AFL-CIO-affiliated locals will decide whether or not it will participate in the one-day walkout, Toohey said. The unions represent 250,000 members, most of whom are working under valid contracts, and their solidarity on this issue is not assured.

"There's no telling how this will turn out," said the council president, acknowledging that the local federation was gambling with whatever political clout it has by approving the strike call. "This is a large city. It's going to be a tremendously large organizational job to put this thing in place by Oct. 28," Toohey said.

The council last proposed a citywide strike in February 1973--again, because of a teachers' dispute. But the Nixon administration pressured the council to abandon the move.

Robert Bonitati, White House labor liaison, said yesterday that the Reagan administration "has a policy of not becoming involved in the collective bargaining process" and would not involve itself in the Philadelphia teachers' strike.

The Philadelphia council's vote caught state and national AFL-CIO leaders by surprise.

"We didn't know about that" until Thursday morning, said Rex Hardesty, a spokesman for AFl-CIO President Lane Kirkland. "That's a local strategy decision. They're perfectly capable of making it. They know their city better than we do," Hardesty said.

Kirkland himself had been under pressure to call a nationwide general strike in support of nearly 12,000 air traffic controllers, federal workers, who were fired from their jobs after going on strike Aug. 3. Kirkland responded by setting up financial assistance and job referral programs for the dismissed controllers. And he featured their cause at the AFL-CIO's Sept. 19 "Solidarity Day" demonstration that brought more than 250,000 people to Washington to protest against Reagan's social and economic policies. But he has steadfastly refused to call a general strike.

"Unlike some movements in parts of Europe and elsewhere, we do not conduct short, political or even economic demonstration strikes," Kirkland said in a Sept. 13 interview with reporters. "It would have to be a matter of the gravest national concern to bring me to the point of undertaking to organize a general strike," Kirkland said then.

The latest Philadelphia teachers' strike was prompted by the layoffs of 3,500 city teachers last summer and the cancellation of a scheduled 10 percent pay raise in apparent violation of a two-year pact between the city and the Philadelphia Federation of Teachers.