If you are a PR in the USA, not only do you have to have ID, but you have to submit something that shows your status. If you haven't (yet) naturalized and therefore can get a US Passport, you need to surrender your I-551 card (and I-797C extension letter if the I-551 is expired) when you check in. I still brought my CDN passport when I went, though, as USCIS had to stamp it when I went through the non-citizen clearance on debarkation morning... All your cruise docs should tell this.