I'm pretty sure that as of 1-1-08, you need a passport to either enter the US or Canada at the Canadian border. I might be wrong, but I have heard that the grace period ended last month.
So, yes, I believe the laws have changed, and while you might still be able to use your military ID to do it, you had better know before you go. Check with your superior officers, and if they can't give you a really certain answer, check with the State Department (online). If you need a passport, you cannot do it online. You need to go to a proper Passport office, and have the proper white-background photo made, etc. Most major Post Offices in the US can take care of it all...The time necessary can vary, If you NEVER had a passport, you need to give it a certain amount of time, less if you can send in your old passport. It only took me about two or three weeks to get a renewal, using the old one. If you can't lay your hands on it, but can get the number, that can help expedite things, as well.
Good luck, maybe all you need is your MID.