Members of Congress from big federal employment centers--and they range from Anniston, Ala., to Ogden, utah, to Manhattan--are furious with the Reagan administration for saying that125,000 government workers could be fired as an alternative to the failure of Congress to approve a 5 percent civil service pay cut.

Some members have calledthe so-called budget option an attempt to blackmail Congress. Others have warned privately that if either action is carried out, it could lead to illegal strikes by federal employes.

Some congressional staffers report that their bosses, most of whom are away from Washington, have reacted angrily to news leaks last week on the job cut option.

One congressional aide, whose boss is in Africa, said that the office had heard from him two days after the story hit the wires. "I think I could see the smoke cloud rising from the east even before we got his call," the aide said.

Rep. Robert T. Matsui (D-Calif.) called the jobs cut proposal "an attempt to extort the Congress." Matsui said the Office of Personnel Management is "telling Congress to go along with this 5 percent pay cut or be responsible for 125,000 people being fired."

OPM's compensation report, officially issued yesterday, said turnover in the federal government is much lower than in the private sector. It said that this is an indication that government employes are overpaid.

It also said that a 5 percent pay cut would begin moving federal salaries "toward market levels" and would be "more humane than the only realistic alternative, the separation of 125,000 employes in order to achieve a spending reduction of the same magnitude."

"The larger problem is that neither the proposed pay cut nor the elimination of federal jobs is a responsible or cost-effective way to reduce the deficit," Matsui said.

Matsui, who serves on the Federal Government Service Task Force, said the jobs cut option is "destructive to morale." He maintained that it "invites confrontation with the federal work force" at a time when those workers are being asked to run key programs with fewer people.

One member of the task force -- which serves as a civil service caucus -- said: "It is one thing for the administration to ask federal workers to bite the bullet on pay. That kind of approach might play with Congress.

"But when you tell a member you are putting him or her on the spot -- either cut pay or be responsible for putting 125,000 people out of work -- you are playing with political dynamite.