The president of the Professional Air Traffic Controllers' Organization (PATCO yesterday all but threatened a nationwide controllers strike when he told Congress that negotiations for a new contract have broken down with the Federal Aviation Administration.

"At this time, I believe the air traffic controllers are becoming angry," PATCO's Robert Poli told the House subcommittee on employe compensation and benefits. " . . . We are not planning a strike, but there is a certain unrest."

Poli's union, with 15,000 of the nation's 17,000 and traffic controllers, has been working without a contract since March 15. Union representatives have had 37 negotiating seesions with the FAA and walked out Tuesday, Poli said. "The FAA response is one of absolutely no movement on any issues we have put on the table," he said.

Poli reporters that if there is no movement by the time his union's executive board meets May 19 "we'll be down to the short strokes." Poli has promised repeatedly that there will be no air traffic control slowdowns, a time-honored PATCO tactic. Instead, he said, "If it comes time, we will act like a labor union."

An air traffic controllers strike would be technically illegal but, as Poli had said earlier, "the only illegal strike is an unsuccessful one."

Transportation Secretary Drew Lewis, the FAA's boss, declined to spell out the Reagan administration's position on PATCO's demands regarding wages-and-working conditions, but told the subcommittee he is "hopeful we will have a harmonious settlement."

Congress must approve most wage and working-condition changes for the controllers, so the FAA cannot technically negotiate anything. However, administration support for a particular wage and working-condition package would improve its chances dramatically, and it is that support PATCO seeks.

PATCO has proposed that controllers work a 32-hour week (instead of 40) and that they be separated from the standard civil service GS pay scale and put on their own pay scale, which would have a top salary of $73,000 for the most senior controllers working in the busiest air traffic centers.

Lewis said the bill would cost the government $1.1 billion in the first year; Poli said it would cost $1.7 billion for three years.

The proposal is embodied in a bill introduced by Rep. William L. Clay (D-Mo.) and was unconditionally opposed by the Office of Management and Budget in a letter to subcommittee Chairman Mary Rose Oakar (D-Ohio). The letter, dated Wednesday, was the first official position the administration has taken on the Clay bill.

Oakar, in a question to Poli, said that Clay's bill, which includes a generous raise plus cost-of-living escalators exceeding the cost of living, would result in a controller making $125,000 annually. "This is two times greater than top government executives receive," she said. "What is the justification for that?"

Poli answered that "it has been a long time sine air traffic controllers have received anything but the cost-of-living increase . . . ."

Oakar said in an interview that "we are concerned about an apparent lack of communication" between PATCO and the administration. She said OMB has yet to send her committee it estimate of the Clay bill's cost and that it is her feeling the PATCO negotiation is not a priority matter in the administration. "My feeling is it ought to be a priority," she said.