I am a new RN waiting to see if the air force is going to take me under it's wing. If you wanted to, the military would undoubtedly have a position for you.
From my experience, unemployment as a new BSN grad even without a license, is due to anything but the job market. You just have to apply at a lot of hospitals especially if you want a job that you are really interested in! A lot of my friends from nursing school
did get jobs before and soon after graduation (may 2009).
Off the top of my head, you could apply to:
Barnes Jewish Hospital
St. Louis Children's Hospital
St. Louis University Hospital
SSM hospitals (DePaul)
The VA hospital
Most if not all of these have online application processes making that much easier! It may take a while for them to get to your application, but you can always call and speak to someone during the week.
If you decide to pursue the military you must have your license prior to commissioning.