The money troubles of Illinois, which faces a roughly $4.6 billion shortfall for the current fiscal year and has been without a budget since July, are real. But the troubles of the Lincoln papers, according to interviews with a dozen people familiar with the project’s history, also stem from the byzantine politics surrounding the Lincoln museum and library, which opened to fanfare in 2005 but has since suffered from declining attendance, outdated exhibits, staff departures and internal rivalries.

Mr. Rauner, a former businessman, and Mr. Madigan have floated differing proposals to separate the museum from the preservation agency. An independent report on the museum released last January opposed a separation but painted a dire picture of an institution whose scholarly functions had been hampered by a “political and bureaucratic culture” and a convoluted governance structure akin to “a ball of spaghetti.”

The Papers of Abraham Lincoln, a joint project of the museum and the preservation agency, has had some financial independence from the spaghetti. Since 2008, less than a third of its roughly $800,000 annual budget has come from the state, with federal grants and private donations making up the rest. Except for Mr. Stowell, who is a state employee, the rest of the staff members are paid through the University of Illinois, which has been a co-sponsor since the 1980s.

But at the September meeting, Amy Martin, the director of the preservation agency, informed Mr. Stowell that the agency would not sign a new contract with the university and was requesting an investigation of the project.

The reason, according to a letter by six members of the project’s advisory board that was sent to the state’s political leaders on Sept. 11, involved questions about two longstanding outside gift accounts that collect private donations to the project. Ms. Martin said that those accounts, which are run by the University of Illinois Foundation and the Abraham Lincoln Association, had not been formally authorized by the preservation agency.

Image A letter from Abraham Lincoln to Edwin M. Stanton, secretary of war. Credit... Papers of Abraham Lincoln

In the letter, the advisory board expressed incredulity that the agency was suddenly “denying” the existence of relationships that had been openly in place for years.