There are several documents you can show your employer to establish your identity and employment eligibility, and employers are not allowed to only accept certain documents within the list of acceptable documents.
Employers are not allowed to ask for specific documents they will accept from a worker and can not prevent anyone from working because of a document's future expiration date.
The Department of Homeland Security has identified different documents you can show your employer to establish your identity and work eligibility. The Form I-9 contains Lists of Acceptable Documents that fall into three categories. Workers are allowed to produce either List A documentation (establishing identity and employment eligibility), or a combination of documentation from List B (establishing identity) and List C (establishing employment eligibility). List A documents include a U.S. passport or passport card, Form I-551 (Permanent Resident Card, Alien Registration Receipt Card, Previous Permanent Resident Card with signature, Permanent Resident Card with the notation "Signature Waived", or Permanent Resident Card with a USCIS-issued sticker extending its validity), Form I-766 (Employment Authorization Document Card), Foreign passport with Form I-94 or Form I-94A with Arrival-Departure Record and containing an endorsement to work, Passport from the Federated States of Micronesia (FSM) or the Republic of the Marshall Islands (RMI) with Form I-94 or Form I-94A, Foreign passport containing a Form I-551 stamp or Form I-551 printed notation. List B documents include a driver's license, ID card issued by federal, state or local government agencies or entities, school ID card with a photograph, voter registration card, U.S. military card or draft record, U.S.Coast Guard Merchant Mariner Document (MMD) card, Native American tribal document, or driver’s license issued by a Canadian government authority. List C documents include U.S. Social Security card, Form FS-240 (Consular Report of Birth Abroad), Form FS-545 (Certification of Birth Abroad issued by the U.S. Department of State), Form DS-1350 (Certification of Report of Birth issued by the U.S. Department of State), Original or certified copy of a birth certificate issued by a state, county, municipal authority or outlying territory of the United States bearing an official seal, Native American tribal document, Form I-197 (U.S. Citizen ID Card), Form I-179 (Identification Card for Use of Resident Citizen in the United States), and Employment authorization document issued by the Department of Homeland Security.