You may be able to apply for a passport card without submitting your passport book.
You must prove both US citizenship and identity in a passport or passport card application.
A passport is commonly used to prove US citizenship, but it isn't the only method. The DS-11 form contains this text applicable to US citizens who were born in the US:
Submit a previous U.S. passport or certified birth certificate. Passports that are limited in validity will need to be supplemented by other evidence. A birth certificate must include your full name, date and place of birth, sex, date the birth record was filed, the seal or other certification of the official custodian of such records (state, county, or city/town office), and the full names of your parent(s).
Thus, if born in the US, you may satisfy the citizenship requirement by obtaining a certified copy of your birth certificate. County recorders can supply such certified copies at moderate cost. (If you were born outside the US, the requirements are different, and may be harder to satisfy.)
As for the identity requirement, the DS-11 says:
You may submit items such as the following containing your signature AND a photograph that is a good likeness of you: previous or current U.S. passport book; previous or current U.S. passport card; driver's license (not temporary or learner's license); Certificate of Naturalization; Certificate of Citizenship; military identification; or federal, state, or municipal government employee identification card. Temporary or altered documents are not acceptable.
As with citizenship, your passport is one way to declare identity, but it is not the only way.
EDIT: note, however, that @phoog has answered below reporting a $35. additional fee for filing a DS-11.