The COVID-19 pandemic has had a significant impact on mental health. Identifying risk factors and susceptible subgroups will guide efforts to address mental health concerns during the pandemic and long-term management and monitoring after the pandemic. We aimed to examine associations of insecurity (concerns about food, health insurance, and/or money), social support, and change in family relationships with poor mental health and to explore disparities in these associations. An online survey was collected from 3952 US adults between May and August 2020. Symptoms of anxiety, depression, stress, and trauma-related disorders were assessed by the Generalized Anxiety Disorder 7-item scale, the Patient Health Questionnaire-9, the Perceived Stress Scale-4, and the Primary Care Post-Traumatic Stress Disorder Screen, respectively. Social support was measured by the Oslo Social Support Scale. Logistic regression was used and stratified analyses by age, race/ethnicity, and sex were performed. We found a higher prevalence of poor mental health among those who were younger, female, with lower socioeconomic status, and racial/ethnic minorities. Participants who were worried about money, health insurance, or food had higher odds of symptoms of anxiety (OR = 3.74, 95% CI: 3.06–4.56), depression (OR = 3.20, 95% CI: 2.67–3.84), stress (OR = 3.08, 95% CI: 2.67–3.57), and trauma-related disorders (OR = 2.93, 95% CI: 2.42–3.55) compared to those who were not. Compared to poor social support, moderate and strong social support was associated with lower odds of all four symptoms. Participants who had changes in relationships with parents, children, or significant others had worse mental health. Our findings identified groups at higher risk for poor mental health, which offers insights for implementing targeted interventions.