Mike Madigan likes to take down names. Two weeks after the 2014 election, Mr. Madigan, speaker of the Illinois House, met Gov.-elect Bruce Rauner for breakfast at the elegant Chicago Club. The two men shook hands, Gov. Rauner recalls, whereupon Speaker Madigan “hands me a 3-by-5 card. It’s got, I think it was seven names. I look at it and, ‘Oh,’ I said, ‘some of those look familiar.’ Any guess what the seven names were on the card? The seven governors he’s outlasted and outmaneuvered.”

Mr. Rauner got the message: “You’re going to be No. 8.”

That remains to be seen—the governor is now seeking a second term—but Mr. Rauner makes clear on a recent visit to the Journal editorial board that Speaker Madigan has proved a formidable opponent of his efforts to reform the state’s government and restore its fiscal health. “If you’re asking any really difficult question,” Mr. Rauner says, “the answer is Madigan.”

Mr. Madigan is a Democrat and Mr. Rauner a Republican, but they are opposites in a more arresting way. Mr. Rauner, 61, is a political neophyte, a reform-minded outsider. He amassed a nine-figure fortune during three decades as a venture capitalist, then got involved in educational philanthropy. “I was recruited to run by the business community in Illinois, because many of them were leaving and the rest of them didn’t want to leave,” he says. “They knew that I was passionate about job creation and free enterprise.”

The 75-year-old Mr. Madigan is the epitome of a career politician. He was first elected to the House in 1970, so this his 48th year as a state representative. He became speaker in 1983 and has held that post ever since, except for the two-year term after Republicans won a majority in 1994. Since 1998 he has also been chairman of the Illinois Democratic Party. In 2012 Chicago magazine called him “the Real Governor of Illinois.”