The correct phone number for obtaining a parking permit is: (520) 877-6000
However, you just go to their WEBSITE to get the permit now!
To get an overnight parking permit, fill out this form: http://webcms.pima.gov/cms/one.aspx?portalId=169&pageId=26888
They'll email you back the permit, and you just print it out. Oh, and it's FREE.