An extension extends filing of the return, not payment of the tax.  If the return is ready to be filed, you could just as well file it.

You can extend the federal and file the state, assuming the state return isnt one that requires the federal to be filed before it can be processed

https://proconnect.intuit.com/support/en-us/help-article/electronic-filing/state-e-file-methods-stan...

So, unless you're IL, you can file a state stand-alone return? Just checking I am reading the article correctly? 

Yes, looks like youre good to go for filing IL alone.

You can file the state as long as you are sure the federal issue will not change the state bottom line. Filing state independently may depend on which state. Check the instructions as to whether it requires the federal to be attached.