The International Association of Fire Fighters is a small union of just under 300,000 members with political influence far beyond its size. The obvious reason for this is the respect many Americans have for firefighters, who consistently rank as some of the country’s most admired professionals. The less obvious reason is Harold A. Schaitberger, a tall, barrel-chested man with meaty hands and rheumy eyes, who has served as the union’s general president for over 15 years. Under Mr. Schaitberger’s stewardship, the biennial fund-raising haul of the union’s political action committee, Firepac, has grown to nearly $18 million from just under $3 million, allowing him to play the role of power broker. The union usually endorses Democrats for president, but this year Mr. Schaitberger met with Jeb Bush to discuss his presidential ambitions. He has a close, longstanding relationship with Vice President Joseph R. Biden Jr. and has been courted aggressively by the campaign of Hillary Rodham Clinton, whom the union made initial plans to endorse before reversing course as a Biden candidacy loomed. The stature of Mr. Schaitberger, who favors chunky cuff links and suits from Nordstrom, and takes home roughly $330,000 a year from the union, has not come cheap. He has a fondness for first-class airfare and chauffeured travel. According to Labor Department filings, the union spends roughly $30,000 a year with a single hired-car service, and officials said Mr. Schaitberger took most of the rides.