For example the Chicago School District..
The Sun Times is reporting that Fitch took the district's credit rating down a notch to single A+ (still investment grade, but every time it goes down it makes debt more expensive) one of the reasons cited was late state aid.
How late, the state still owes CPS $164 million from last year and is late on $206 million this year.
The City of Chicago...
Bond Buyer is reporting that
Chicago has stepped up its investor-relation efforts as it seeks to minimize the premium demanded by buyers of paper from Illinois-based borrowers, due the state's liquidity and budget crisis
Chicago also put a $804 million bond issue on hold waiting for a more 'Opportune Time'. So it would seem thee city was not happy with the rates it was looking at. The other part of this is that $214 million of that (according to Bloomberg) was going to be taxable Build America bonds.
There is a chance the Build America bond program may not be extended (read the whole story), if it is not extended during the lame duck session. Then it will be up to a Republican controlled congress to extended it, which is going to be less likely.
So imagine that it is not extended during the lame duck session, there will likely be a host of government entities who may try to issue these bonds before the program ends, creating additional supply that Chicago will have to deal with and may get priced into the bonds (the interest rate).
So there you have it, the late payments might be handy for the budget but they are hurting the rest of the state.