I hear you Tripod, especially having worked for a state government agency before, I know things run very very slow.
However according to the USMLE Representative at FSMB who I spoke with online, and their website, if you apply online, you're application will be processed 3-5 days after receipt of the signature card. Then your scheduling permit will be mailed within 5 days after that.
Here is an excerpt from their website:
4) When should I request an application?
The completeness of your application and any accompanying documentation, along with the volume of application requests currently being processed, will determine how long it will take to process your application. Allow FSMB approximately 2-4 weeks processing time if submitting the paper application. If applying online, your application should be completed within 3-5 business days after receipt of the photo id/signature page (and any other required documents) that you will have to mail to FSMB after applying for Step 3 online. Your scheduling permit will be mailed within five business days after processing is complete.
6) Is postgraduate training required to sit Step 3?
Most states require that an individual have completed a portion of their postgraduate training prior to sitting for Step 3. However, the following states do not require postgraduate training to sit for Step 3:
Arkansas Louisiana*** New York Utah* Wyoming**
California Maryland*** North Carolina** Virginia
Connecticut Nebraska* South Dakota Washington Osteo
Florida Nevada Texas West Virginia
*valid, indefinite ECFMG certificate required for international medical graduates
**applies only to domestic medical graduates
***Training required at fourth attempt
7) How do I register for Step 3?
This will depend upon the medical licensing authority for which you are sitting the exam. Contact the Federation directly at (817) 868-4041 for specific information on how to register for the examination.
8) Will I be required to apply for a medical license when I apply to take Step 3?
The following licensing authorities require that you apply for licensure at the same time you are applying to take Step 3: Alabama, District of Columbia, Idaho, Illinois, Kansas, Michigan, Mississippi, Missouri, New York, North Carolina, Oklahoma, South Carolina, and Wisconsin.