On the sticky question of how to fire a federal worker, a House committee yesterday handed the Carter administration a victory for its civil service revision bill by defeating, 15 to 10, a labor-supported amendment that would give federal employes the right to a hearing before they can be fired and taken off the payroll.

Under present personnel rules, employes can be fired without a hearing but they have the right to appeal through several levels afterward - a process that administration officials say should be streamlined.

In a markup session before the House Post Office and Civil Service Committee, Stephen Solarz (D-N.Y.) introduced an amendment calling for "pretermination hearings." He said it wah a means of removing the "opportunity for endless delay" in the present system of appeals by requiring an agency to hold the hearings within 90 days of its decision to fire someone.

If the employe were found to be using delaying tactics, Solarz said, "he could be terminated in 90 days anyway," without the hearing.

Committee vice chairman Morris Udall (D-Ariz.) opposed the amendment on the grounds that it "goes in the opposite direction from the president's goals. Instead of giving management more flexibility," he said, it would give "more protections for employes."

On the controversial question of veterans preference rights, lobbyists for both the administration and veterans groups were saying the vote in the committee will be close.

The committee postponed until next week a vote on that issue that had been expected yesterday. Administration lobbyists said the vote was put off because opponents of the president's proposed changes "knew we had the votes." Some committee sources however, said they doubt that assessment.

The president's plan, defeated recently by a Senate committee, would curtail advantages for most able-bodied veterans in federal hiring and job retention, but would maintain or increase those benefits for Vietnam era and disabled veterans.

President Carter has been writing and telephoning members of the committee to argue his position on the issue.