Yes, if you are a US citizen, you need a US Passport for cruises to Alaska. I was surprised, too. The regular wait for a passport is 4-6 weeks but because it is summer, the wait can be longer. You can get the process expedited. I went to the post office and the total for an expedited application was $185.20 (the regular application fee of $62, $65 for the expedite, $13.65 postage both ways and $30 for a processing fee, plus a money order fee). Don't forget to bring two passport pictures. The post office I went to was supposed to be able to take the pictures but their camera was broken. If you don't have a passport, you can't board the ship. Good luck.
I'm taking the Alaska cruise out of Seattle on June 30. What cruise are you going on?