We leave 6/18 on the Inspiration. We applied for passports 3/13 and after 12 weeks as of yesterday, have not yet received them. The Passport website is "http://travel.state.gov/passport/about/npic/npic_898.html". Which you can navigate to a 'Check the status' area and find a generic "... is being processed" type message.
If you are traveling within two weeks, you can call them at 1-877-487-2778 to talk to a live person. Have patience thru the LENGTHY messages and prompts, but you will get there.
As of this morning ours are 'waiting for a completion date and to be shipped'. Which apparently means within the next couple of days.
Passport requirements and information can be found at the 'travel.state.gov' site.