You can cut several days or even weeks off the total turn-around time by staying involved with how your application is going through the permit process at your local jurisdictions.
Did you meet with the members of the different departments that are involved in approving your project prior to submitting your project documents? You should have told them at the pre-design meeting what your anticipated date is for the beginning of construction. They can help you meet your schedule if you ask them to work with you.
Some jurisdictions will let you defer some of the submittal documents so your project can begin the review process quicker. Ask about this. You could save weeks with just this one little trick. Maybe just the civil drawings could be submitted first for review. The land use issues generally take the longest anyway.
If the jurisdiction has an on-line tracking system, check the progress at least twice a week. Use the e-mail address of the current reviewer as a tool to check the progress. If something is not happening with the review on your project at least weekly, you should be sending an e-mail to the reviewer asking what the time for completion of his review is.
Another thing to remember is that project documents get lost quite often while in the review stages and you should be on top of things to make sure your documents do not disappear while in the review process. Lots of phone calls and lots of e-mails might make you a pest, but it will get your project through faster.