CHICAGO—Republican Gov. Bruce Rauner is dropping thousands of dollars into the campaign accounts of every GOP lawmaker in Illinois as the state’s fiscal crisis grows and deadlines near.

The $400,000 dispersed in recent weeks appears to be just a start for the former private-equity executive. Since the November election, Mr. Rauner and a few prominent donors—including hedge-fund chief executive Kenneth Griffin of Citadel LLC and real-estate investor Sam Zell—have poured more than $25 million into political committees that are expected to help the governor in his growing battle with Democrats, who control the state legislature.

The stakes only got higher when the Illinois Supreme Court this month rejected a plan to save tens of billions of dollars by reducing pension benefits for state workers and retirees. The ruling is helping to fuel a growing fiscal crisis for the state and its largest city, with Moody’s Investors Service recently downgrading Chicago’s debt to junk.

Across the country, governors and big-city mayors have come to rely on more than the bully pulpit to push their policy priorities. A decade ago, former California Gov. Arnold Schwarzenegger spent heavily on a series of ballot initiatives to try to tackle that state’s financial crisis. More recently, a group run by former campaign aides of New York City Mayor Bill de Blasio helped push his expansion of pre-K.

Still, Mr. Rauner’s fundraising stands out nationally for its size and coming so soon after the 59-year-old governor, who made his fortune at private-equity firm GTCR LLC, ousted incumbent Democrat Pat Quinn.