score:13
You are actually asking two separate questions:
There was a time when US citizens could come into Canada without a passport, with drivers licenses and such like. It's possible that at the cruise terminal you could get by with less than a passport. Here is the CBSA advice. Note the birth certificate to prove US citizenship along with the drivers license to prove you are the person named on the birth certificate. If your name has changed since you were born you'll need paperwork to establish the identity chain. I wouldn't risk it myself, but the worst case here is that you aren't allowed to go have your day trip. US citizens don't need visas to visit Canada, but without a passport, how do the border people know you're a US citizen? It's not a requirement for boarding cruise ships, getting drivers licenses, and so on.
The second case is much more serious. You want to be sure you will be let back in. Current rules say that if the cruise starts and ends at the exact same US port you don't need a passport, even if it stops in other countries. Essentially they are trusting the cruise ship not to take on random passengers in the foreign ports and help them enter the US. That said, they still recommend you have a passport just to make life smoother. (Here's Carnival's page on the topic - you can probably find a similar page on the site of the cruise provider you're considering.)
So if there is a reason why just getting a passport isn't an option, the cruise isn't impossible (US businesses have found ways to deal with the fact people just won't get passports) but life will be smoother if you have one. I'd recommend getting one.
Upvote:-1
You have not stated your country of origin. If you are a US citizen there is no objection for both as US citizens do not require any authorization to enter or exit Canada. Re: visiting Alaska, the state is in USA and so you can visit or remain there as long as you can.
Upvote:2
The embarkation officer in Seattle will deny boarding of an Alaskan cruise if you do not provide either a passport or other accepted proof of citizenship, such as a US state or city-issued (not hospital-issued) birth certificate and driver's license. It is not at the discretion of the cruise line whether to let you onboard if you do not have the required documentation. People are denied boarding even if they say they will stay onboard the ship when it stops in Canada – they will simply not let you go if you do not have the right documents.
If you do travel with only a US birth certificate and driver's license, and some emergency arises while you are in Canada, note that you will not be able to fly back into the US (you would have to get back by land or sea). You will likely be required to sign a form when you check-in that states you understand these risks of travelling without a passport. This is why it is strongly recommended to travel with a passport.