You've asked a lot of questions in one. Yes there are consequences to late filings, but it depends on what the filing or discovery is, how late it is, and whether there's an excuse for the late filing. If you're late on a filing, you should speak to a lawyer.
See Illinois Supreme Court Rule 183 (http://www.state.il.us/court/supremecourt/rules/Art_II/ArtII.htm#183). While there should be compliance with all deadlines, that is especially true with respect to requests to admit, as the failure to strictly comply there can be fatal to one’s claims, even in the wake of Vision Point of Sale v. Haas 226 Ill.2d 334 (2007) and its progeny, which lessened the perceived draconian nature of the rule by clarifying that a trial court has more leeway and latitude when deciding whether an extension of time should be allowed. The rule governing requests to admit is self-executing, though most litigators tend to bring a motion to deem facts admitted where there has not been compliance. I strongly encourage you to sit down with an attorney and all relevant documents to discuss. Good luck!
Robert T. Kuehl
Kuehl Law, P.C.
Depends on a number of factors, including severity of your violation, prejudice to opposing side, if you have a "meritorious defense" for being late, whether you acted diligently in curing your discovery delays.
You must have a timely petition and a state good cause. The Court will consider your history. Illinois public policy is to settle disputes on "merit" not technicality--so this favors you.
However, the Court will grow wary of missed deadlines if they are repeated--so count your blessings and don't be emboldened by extension.
As for Request to Admit, failure to timely respond used to be a death sentence of sorts. Since then, the law has evolved and the Judge has more discretion to give you breathing room.
The author provides the preceding information as a service to the public. Author's response, as stated above, should not be considered legal advice. An initial attorney-client conference, based upon review of all relevant facts/documents, will be necessary to provide legal advice upon which the client should then rely.