Yes, normally if your current driver's license is suspended then you can apply for a state non-driving card to use as valid proof of identification, often referred to as an identification card.
For example the State of Michigan's SOS states that one is eligible for a state identification card if their Michigan driver's license has been suspended, revoked or restricted. Residents with a document granting them permission to drive but lacking their photograph, such as a Temporary Instruction Permit, restricted license ordered by the court or Secretary of State or a 625g paper permit, are also eligible for a state ID card.
To obtain a state ID card in MI one must visit a Secretary of State office. You will need to provide documentation of a valid Social Security number, U.S. citizenship or legal presence, identity along with at least two documents establishing Michigan residency before a state ID card will be issued. All documentation is subject to Department of State approval. In some cases, document approval may not occur in the same day and may require an additional visit. There is a $10 fee for state ID cards. Your ID card will expire four years from your last birthday.
[Let CarInsurance.com help you find affordable auto insurance now.] As another example, in New York State a person of any age who does not have a driver license can apply to the DMV for a non-driver photo ID card. You must provide acceptable proofs of identity and date of birth. You can also apply for a non-driver photo ID card if your NYS driver license is suspended or revoked.
When you apply for a non-driver photo ID card in New York you must surrender your NYS driver license. There are no exceptions. You do not however have to surrender a non-driver photo ID card when you get a driver license or your driver license is reinstated.
In NYS a non-driver photo ID card contains the same personal information, photo, signature and special protection against alteration and fraud as a photo driver license. To get more information, read the NYS DMV brochure on Non-Driver IDs.
Requirements to obtain a State Identification (ID) card differ by state so you will need to check with your state's Department of Motor Vehicles to see what steps to take to get a state ID card to use as valid piece of identification while your state driver's license is suspended.
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In case it takes time for your DMV to verify information and thus delay you obtaining your state non-driving ID we would advise you contact them as soon as possible so you can have this valuable piece of identification and be able to obtain the passport for your cruise.
As you are likely aware, to obtain a passport for the first time, you need to go in person to one of over the passport facilities located throughout the United States with two photographs of yourself, proof of U.S. citizenship, and a valid form of photo identification such as a driver's license of state ID. While the passport office was backlogged for awhile according to the US Department of State currently they are processing routine applications in less than four weeks from the time of application. If you choose to pay more for expedited service then you may be able to receive your passport in two weeks. | 
