I suppose the first question is: Was your security clearance revoked while you were in the military/being discharged? If your job routinely included handling classified material, then if your clearance was revoked you should have been informed. On the other hand, I'm not certain what procedures are for people who have a clearance but not access (by default, every commissioned officer in the US military has a 'secret' clearance).
At any rate, when you go to process your civilian clearance your discharge is going to be a huge question that needs to be adjudicated. Security clearances are given on a "case by case" basis, based on the results of the security investigation. There are guidelines for the adjudicators, and you can find them on the web at:
http://www.dss.mil/nf/adr/index.htm
The key here is your assertion that your record/conduct are otherwise "spotless". If so, that can make up for a lot of things. On the minus side, however, your misconduct was apparently very recent. Your discharge was not punitive, and was under honorable conditions, but there was misconduct. If it had happened 5 or 10 years ago I'd say you had a very good chance for a secret or even TS. If you only recently got the discharge, however, it becomes a bit more dicey.
So I'd say it could go either way. One key, as always, is to be very truthful and forthcoming on paperwork and in particular if you talk to an investigator. Lies by omission will get you in trouble fast, so if there are embarassing details, etc. then steel yourself to disclose them openly right up front.
As an aside, does your potential employer know about your discharge? If they do, and don't care, fine. But they may suddenly decide they don't want to hire you either directly because of your general discharge or because they fear you will not get the clearance (regardless of whether you get your clearance, they will be charged for the investigation). Clearances and jobs can raise very tricky questions about employment law.