I am in Utah to work for a small employer with about 10 employees. The company is talking about downsizing and im one of the newer workers. Would I qualify for the health insurance?

Probably. Participants with under 20 employees can qualify for 12 months under Utah's mini COBRA Law http://www.cobrahealth.com/Mini-State-Laws/Utah.html

Were you fired for gross misconduct? Work for a church related organization? Are they talking about eliminating the health plan alltogether? If so, COBRA continuation, might no be available, depending on Utah state law.