Yesterday, the EEOC published its guidance on the COVID-19 vaccine under the ADA and GINA, in the form of nine Q & As. You can read them in their totality here.
The TL;DR: yes, you can force employees to receive the COVID-19 vaccine as a condition of employment (although the should is an entirely different issue), subject to limits on reasonable accommodations for employees' disabilities and sincerely held religious practices or beliefs and subject to limits on pre-vaccination medical questions.