CHICAGO — The Democrats, who run this state, regularly fret over Illinois’s financial woes — the unpaid bills, the mortifying credit ratings, the benefits cuts to save one of the nation’s most underfunded pension systems. But then there is the dream of becoming home to Barack Obama’s presidential library, which is, it seems, a whole different matter.

“In this case, we’re talking about a son of Illinois who became president of the United States,” Michael J. Madigan, the longtime Democratic speaker of the Illinois House, said on Wednesday, urging fellow lawmakers to pledge $100 million in state money as a way to help lure the presidential library here — and away from other states with claims on the president’s history, like New York and Hawaii.

Institutions and groups vying to host this presidential library have until June 16 to submit details to the Barack Obama Foundation. And former colleagues here, in the city where Mr. Obama still owns a home and where people here had long presumed the library would surely land, are making it clear they intend to leave no part of this competition to chance.

Republicans do not see it that way. “The Democrats are putting up five or six different income tax hike proposals — all under the guise that we don’t even have enough money to run basic state services, but then let’s find $100 million for the library?” said Jim Durkin, the Republicans’ House leader. “I’m just baffled. I’m dumbfounded.”