“I’m a business guy,” Mr. Rauner said last week after appearing in a final forum beside his three Republican rivals — two state lawmakers and the state treasurer. “I’m not a politician.” So far, he has invested $6 million of his own money in a campaign that has dwarfed everyone else’s.

For more than a decade, Democrats in President Obama’s home state have maintained single-party control of the governor’s office and both chambers of the Legislature. Yet the contest to defeat Gov. Pat Quinn, the Democratic former lieutenant governor who replaced Mr. Blagojevich and who is pressing for a second, full term, is now viewed by Republicans as perhaps the strongest chance in the nation to seize a governor’s office from Democrats.

“It’ll be a rock ’em, sock ’em campaign,” Mr. Quinn acknowledged last week as he left a church basement in Chicago’s Pilsen neighborhood, where he was promoting efforts to raise the state’s minimum wage. “This is a tough state politically,” said Mr. Quinn, whose approval ratings, at times, have dipped to miserable lows.

Still, Mr. Quinn, 65, who was once viewed as more of a quirky, rumpled gadfly than a polished powerhouse destined for the state’s highest office, has shown a pattern of surviving predictions of his demise.