The effectiveness of COVID-19 vaccines depends on widespread vaccine uptake. Employing a telephone-administered weighted survey with 19,502 participants, we examined the determinants of COVID-19 vaccine acceptance among adults in Texas. We used multiple regression analysis with LASSO-selected variables to identify factors associated with COVID-19 vaccine uptake and intentions to receive the vaccine among the unvaccinated. The prevalence of unvaccinated individuals (22%) was higher among those aged 18–39, males, White respondents, English speakers, uninsured individuals, those facing financial challenges, and individuals expressing no concern about contracting the illness. In a fully adjusted regression model, higher odds of being unvaccinated were observed among males (aOR 1.11), the uninsured (aOR 1.38), smokers (aOR 1.56), and those facing financial struggles (aOR 1.62). Conversely, Asians, Blacks, and Hispanics were less likely to be unvaccinated compared to Whites. Among the unvaccinated, factors associated with stronger intent to receive the vaccine included age (over 65 years), Black and Hispanic ethnicity, and perceived risk of infection. Hispanic individuals, the uninsured, those covered by public insurance, and those facing financial challenges were more likely to encounter barriers to vaccine receipt. These findings underscore the importance of devising tailored strategies, emphasizing nuanced approaches that account for demographic, socioeconomic, and attitudinal factors in vaccine distribution and public health interventions.