Fairfax County's 7,154 teachers return to the classroom Tuesday facing a crucial test of their own clout in the schoolhouse and at the ballot box.

At stake are demands -- already branded foolish by some politicians -- from the militant, 6,500-member Fairfax Education Association for sharply higher teacher pay. The FEA says that inflation has eroded their pay and they need a 20 percent pay boost in 1980 to catch up.

Angered by last year's 5.13 percent pay raise, the association voted last week to continue a controversial job action designed to slow extracurricular school activities. More importantly politically, say some, is the decision by the teachers' political action committee to plunge directly into this fall's county elections with financial support for the eight supervisor candidates who have promised support for higher teacher pay.

That action and the $157.1 million price tag school board officials have put on the teachers' demands already have become an issue that some politicians say could backfire on the teachers in the Nov. 6 election.

The candidates say taxes are the major worry of Fairfax voters this year and the teachers' demands fly in the fact of that.Furthermore, they question whether the teachers' promise to work to the letter of their contracts, thus avoiding any after-hours volunteer chores, won't further cut into public support for the teachers.

None of the eight FEA-endorsed candidates for the Board of Supervisors specifically has backed the teachers' 20 percent pay raise demand, but all eight answered a questionnaire in favor of higher teacher salaries.

One of the eight, D. Patrick Mullins, denounced the proposal as "catastrophic." The other endorsed candidates are incumbent Martha V. Pennino and James Scott, and challengers Sandra Duckworth, Carl Ericson, Betsy Hinkle, Maya Huber and Vivian Watts.

Republican Board Chairman John F. Herrity figures that the entire FEA package would cost the typical Fair-whether the teachers there can be as fax homeowner $832 in higher property taxes and he says that's too much. "We're in a highly volatile economy," he said. "I don't believe it is in the public interest to trade [an endorsement for] that kind of commitment."

Democratic Supervisor Alan H. Magazine, who is not seeking reelection but has run with teacher support, said the demands "could be counterproductive. There are other demands politically, especially by the middle class, to lower real estate taxes," he said.

Democrat Vivian Watts, who is running against Herrity with teacher backing, is openly critical of the FEA's job action. "Extracurricular activities are an extremely important part of education" in Fairfax's huge school system, she said. "It's regrettable that the job action continued, but I guess it's better than a strike."

Even if the job action succeeds this year -- and there is much debate about its impact last spring -- some Fairfax politicians are doubtful politically effective as some teacher groups elsewhere in the Washington area. The Fairfax teachers won't say how much money they've raised thus far but say they are seeking $15 donations from each FEA member, which would give them $97,500.

"In the past, teachers have not been a political force in the county, said Emilie Miller, head of the Fairfax Democratic Party. "They would endorse candidates, but not be involved in campaigns as a group.

"But this year they seem more determined," she said. "We'll have to see whether this can be translated into action."

Gerry Gripper, president of the FEA, argues that the teachers "had no choice, but to get involved" and lobby for their share of county funds. Starting pay for Fairfax teachers is about $11,000 a year and the typical teacher is earning $18,500 -- not enough, Gripper says, to cope with the costs of living in affluent Fairfax.

Adding incentive for the venture into politics has been Virginia's ban on collective bargaining agreements, Gripper said. That gives the Fairfax teachers far less leverage than teachers in the District of Columbia, where there is a strong teachers' union, and forces the suburban teachers to turn to the political process to resolve their demands, he said.

The Fairfax teachers' efforts this June at backing state legislative candidates in party primaries was tinged with caution. The $5,000 the teachers raised was apportioned among candidates that the group believed were certain of winning their races, Gripper said.

"We didn't want to dilute our power," Gripper said, somewhat apologetically. All the teacher-endorsed candidates won.

Donna Poll, chairman of the teachers' political arm, Political Action Committee for Educators, said that 700 teachers have already volunteered to work in Watts' campaign against Herrity. But thus far few of them have showed up at Democrat Watts' headquarters, the candidate said.

"I have three or four workers from the party and one is a teacher who works a couple of hours at any one time," she said. "But it would be generous to say teachers [are the only political] workers."

Despite the skepticism, the politicians aren't willing to write the teachers off this fall. Republican Mullins says the only teachers he has seen "were on the other side of the doors of the houses I canvassed. But that could change after Labor Day when everyone is back to school."