As the COVID-19 pandemic drags into its second year, there is hope on the horizon, in the form of SARS-CoV-2 vaccines which promise disease suppression and a return to pre-pandemic normalcy. In this study we critically examine the basis for that hope, using an epidemiological modeling framework to establish the link between vaccine characteristics and effectiveness in bringing an end to this unprecedented public health crisis. Our findings suggest that a return to pre-pandemic social and economic conditions without fully suppressing SARS-CoV-2 will lead to extensive viral spread, resulting in a high disease burden even in the presence of vaccines that reduce risk of infection and mortality. Our modeling points to the feasibility of complete SARS-CoV-2 suppression with high population-level compliance and vaccines that are highly effective at reducing SARS-CoV-2 infection. Notably, vaccine-mediated reduction of transmission is critical for viral suppression, and in order for partially-effective vaccines to play a positive role in SARS-CoV-2 suppression, complementary biomedical interventions and public health measures must be deployed simultaneously.