Outraged parents have circulated petitions, the School Board is deadlocked on the issue and even supervisors from across Fairfax County are getting into the fray.

The issue? Not budget cuts, nor teacher salaries, nor even how long the school day should be. It's whether the gymnasium at Waynewood Elementary School should be carpeted.

In these times of anxiety over dwindling tax revenue and political turmoil over Superintendent Robert R. Spillane, the Fairfax School Board tonight will revisit one issue it can't seem to resolve. After rejecting a request to exempt Waynewood from the carpeting program last month, the School Board is expected to reverse itself tonight at the behest of several supervisors who have no constituents living in the area.

"This is something that should've been worked out with the community," said Supervisor Thomas M. Davis III (R-Mason). "If they don't want it, why put it down?"

For the last year, parents of children at Waynewood, which is in the Fort Hunt area, have campaigned vigorously to keep the school system from installing nylon all-purpose flooring known as Pro-Gym at the school, complaining that it wouldn't be conducive to after-school basketball or roller skating and could cause injuries.

School officials maintain the carpet makes the gyms more versatile and comfortable, and said there have been no complaints from the 40 schools that have been carpeted.

Last month, School Board member Armando M. Rodriguez, whose Mount Vernon District includes Waynewood, asked his colleagues to grant an exception for the school, but his motion failed on a tie 5-to-5 vote. Two board members who voted against the exemption, Carla M. Yock (Mason) and Joanne T. Field (Dranesville), are expected to switch their votes tonight.

Yock said she would do so as a favor to Davis, who appointed her, but that it leaves a bad taste in her mouth.

"This is a non-issue that just won't die," she said. "I don't like this because we can't have every little community for every little school decide the floor covering and desk coverings and color of the tiles for everything. We've got a process."

Some school officials complained that supervisors are playing election-year politics with the issue, jockeying to see whether Democrats or Republicans can take credit for satisfying the community.

Davis denied that, saying he only got involved because Supervisor Gerald Hyland (D-Mount Vernon) asked him to talk with Yock.

Davis, who said the school system has created "bureaucratic rationales" for ignoring community wishes, has no constituents involved, although he is planning to run for the countywide Board of Supervisors chairmanship this year.

"I'm not playing politics with this thing," he said. "I don't think that has any place in this."

Nevertheless, Waynewood parents are grateful for any aid. They have collected 384 petition signatures against the carpeting and even School Board Chairman Kohann H. Whitney (Centreville) conceded that no one from the community has asked for it.

"In a democracy, do the people who are most affected by the decisions have a voice?" asked Stephen Fitzgerald, a parent and coach with the Fort Hunt Youth Athletic Association, which uses the gym. "Or is government so remote that it can't hear what the people affected have to say?"

Spillane stood by the carpet as the best for a multipurpose room, but before last month's board vote, he said that "the community has made an excellent case," and he did not object to leaving Waynewood with a tile floor.

"I don't think lightning will strike or the foundations of this building will crumble if we make an exception," he said. Budget Woes May Be Worse

Fairfax school officials, already expecting a deep cut in the aid they receive from the state, now say it will be even worse than previously announced.

Last month, Gov. L. Douglas Wilder (D) announced that Fairfax would receive the maximum cut of 12 percent in state aid, $21.7 million, or about 2.4 percent of the overall school budget.

This week, school officials said they later were told it actually would be a $26 million cut.

In the budget he presented to the School Board last week, Spillane projected a $20 million cut, and he now will have to find somewhere to save money to balance the proposed budget before the board votes on it next month. New Personnel Director Named

Spillane has named a personnel director to replace Edward W. Carr, who left last summer for a senior position with the Virginia Department of Education.

Alan E. Leis, who has been acting assistant superintendent for personnel since Carr's departure, won the job permanently after the School Board endorsed Spillane's selection last month.

In the key position, Leis will manage a work force of 22,700 full- and part-time employees who make the public school system the largest non-federal employer in Northern Virginia and handle sometimes testy relations with two outspoken teacher unions.

A longtime administrator in Fairfax, Leis had served as executive assistant to Deputy Superintendent Jay D. Jacobs, helping him oversee operations of the county's 188 schools and centers.