I know this post is a little old, but I want to add my thoughts.
Why would you want to travel without a passport? The cost of applying for a passport is low when you compare it to the cost of your cruise. The time to get a passport is minimal in the USA.
Once you return from Alaska, you are going to be addicted to cruises and ready to plan your next adventure. You need a passport for almost every other cruise, so just go ahead and do it now.
If anyone reading this thread is even thinking about going on cruises, the time to apply for your passport is today. Just drop by your local post office, pickup an application, and follow the directions.