CHICAGO (Reuters) - Illinois has won some breathing room from Deutsche Bank <DBKGn.DE> regarding the potential termination of an interest rate swap agreement that could cost the cash-strapped state nearly $99.2 million, according to a state document released late on Monday.

In a supplement to the prospectus for its Thursday sale of $550 million of general obligation bonds, Illinois said the bank has agreed to lower the credit rating threshold that would trigger the swap deal's termination.

As the state's ratings inch toward "junk" on the credit scale, the renegotiated Deutsche Bank swap would terminate if Illinois' rating were to fall below BB-plus with Standard & Poor's or Ba1 with Moody's Investors Service.

The state has swap deals with four other banks with termination triggers at the original levels of below BBB with S&P and below Baa2 with Moody's, at a potential cost to the state of nearly $60 million.

Those swap counterparties are AIG Financial Products Corp, Bank of America, Merrill Lynch Capital Markets, and JP Morgan Chase.

Last week Moody's dropped Illinois' rating to Baa2, just two steps above "junk," while S&P cut it to BBB-plus. The credit rating agencies cited the nearly year-long political impasse, which has left the fifth-largest U.S. state without a fiscal 2016 budget and strained finances.

Over the past two months, Illinois hired consultants at a two-year cost of $525,000 to reduce the state's exposure to potentially costly bond-related agreements with banks related to $600 million of variable-rate bonds the state issued in 2003.

Illinois also faces the expiration of six bank direct-pay letters of credit backing the variable-rate bonds on Nov. 26. If the facilities are not renewed by the current banks or replaced by other banks, the state could be forced to pay off some or all of the bonds before their 2033 maturity.

The letters of credit are from JP Morgan Chase Bank, PNC Bank, Wells Fargo Bank, State Street Bank and Trust Company, Royal Bank of Canada, and The Northern Trust Company.

Republican Governor Bruce Rauner, meanwhile, said on Tuesday he was uncertain how a nearly year-long budget impasse would impact Thursday's bond sale but insisted bond buyers are backing his effort to tie his union-weakening, business-friendly agenda to passage of a budget.

"The reforms we’re advocating are supported by investors, and they believe in our administration and the potential future for Illinois," he told reporters.

(Reporting by Karen Pierog and Dave McKinney; Editing by Matthew Lewis)