A federal board which, in its efforts to require that federally funded buildings be accessible to the handicapped, has been criticized as overzealous and targeted for extinction by Reagan budget cutters found an important friend on Capitol Hill yesterday.

He is Rep. Adam Benjamin (D-Ind.), chairman of the House Appropriations subcommittee handling the $2.3 million budget request for the Architectural and Transportation Barriers Compliance Board. If there is anyone in Congress with a chance of winning a fight with the whiz kids in the Office of Management and Budget, it is a House Appropriations subcommittee chairman, who gives the budget its basic shape as it starts through Congress. Benjamin thinks the board should be kept in business.

The compliance board was created by Congress to ride herd on federal agencies that have been slow to carry out provisions of a 1968 law requiring ramps, elevators and other aids in new or remodeled federally financed buildings to help the handicapped move freely in and out.

The board, half of which are public members and several of them handicapped, spent all last year writing guildelines that agencies must meet and published them in the Federal Register four days before Ronald Reagan became president. This meant Reagan couldn't freeze the regulations, but opponents, who include some federal agencies that consider them to rigid and telephone companies that object to a requirement that pay phones be lowered for use by persons in wheelchairs, raised a howl and OMB told the board it will try to wipe out its budget fgor next year.

The board's chairman, Mason Rose, a lawyer confined to a wheelchair for 15 years as a result of an accident as a Marine pilot, told Benjamin's subcommittee yesterday that opponents have exaggerated costs and misrepresented the way the guidelines were filed. The board had been under pressure to get its guidelines published last year, and the fact that they were issued in mid-January meant that they had been slightly delayed, Rose said. Asked why OMB was trying to put the board out of business, he replied: "They very nature of our job is to tamper with the system and the system doesn't like to be tampered with."

After the hearing, Benjamin told a reporter he thinks the board should be kept in operation because it carriers out the law in the most cost-effective manner. Without it, he said, individuals could sue under the 1968 law for a lack of access and cost the government more in the long run.