Hardball politics is nothing new to Robert E. (Bob) Poli, the president of the Professional Air Traffic Controllers Organization (PATCO) who has taken on the Reagan administration with a nationwide strike.

He got to his present position by playing it tough.

John Leyden, who now runs the AFL-CIO's Public Employe Department, remembers a big political game last year in which Poli left him battered and bruised.By Leyden doesn't like to talk about it. Poli's victory, his rise to the PATCO presidency, put Leyden of out of a job.

"That was a very emotional time for everybody. Few emerged from that period unseathed, including Bob," recalls Betty Griffith, a friend of Poli's since 1973 and an assistant to David E. Siegel, PATCO's southern regional vice president.

The union in 1980 was looking for a hard-liner to lead it in what everyone knew then would be a tough contract fight this year. Poli and Leyden were friends, and Leyden was a respected union chief. But many in PATCO thought Poli was tougher.

Poli, then executive vice president of PATCO, and Leyden, then president, resigned their respective positions at an executive board meeting in Chicago after Poli had made known his intentions to take over Leyden's seat. The board met behind closed doors while Poli and Leyden waited outside. When the doors were opened, the board told Leyden that it had accpeted his resignation and rejected Poli's offer.

A few months later, Poli was elected president in his own right.

Since then, the hefty Poli has become something of a folk hero among his members. He is regarded as highly credible: "He's going to do what he says he's going to do," says Richard M. Boyer, another PATCO member and friend of Poli since 1972. "The man is also very intelligenty and articulate. I'm proud when I SEE HIM ON TELEVISION," SAYS paul Amato, a PATCO official in New York.

"I'm no Pied Piper," Poli said yesterday. He was referring to the 13,000 controllers he pulled out on strike at 7 a.m. Monday. He said 12,172 were still on strike yesterday afternoon, even though nearly half of them had been sent job termination notices by the Federal Aviation Administration.

"It's the people out there who are keeping this strike going," Poli said. "They've made this thing."

At 44, Poli is about eight years older than the average air traffic controller. But he is similar to them in many ways. Like most of his members, he is a high school graduate, from Wilkinsberg School near his home in Pittsburgh. He became an air traffic controller in the military, the Air Force in his case. He finished military duty as a staff sergeant.

Poli has worked at flight towers in Pittsburg and Cleveland. He says he knows what his members are talking about when they complain about stress. "His people," as many of them refer to themselves, believe him. a

Poli also says he is aware of the irony of his situation, being the first of only a few union leaders in 1980 to break ranks with organized labor and endorse Ronald Reagan. He refuses to complain about or apologize for that. Instead, he says, "I think the president has been ill-advised on this thing. I don't believe it's been him, more than it's been the people around him who have been pushing" the administratiion's drive to break the illegal strike.

As for his own future: "I don't want any notoriety at all. All I want is a contract for my people and to go back to the regular work of my union," said Poli, who is planning to marry travel agent Diana Kirkpatrick, 31, in September.