Although mRNA vaccines encoding the spike protein of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) prevent COVID-19, the emergence of new viral variants jeopardizes their efficacy. Here, we assessed the immunogenicity and protective activity of historical (mRNA-1273, designed for Wuhan-1 spike protein) or modified (mRNA-1273.351, designed for B.1.351 spike protein) Moderna mRNA vaccines in 129S2 and K18-hACE2 mice. Mice were immunized with either high-dose or low-dose formulations of the mRNA vaccines, where low-dose vaccination modeled suboptimal immune responses. Immunization with formulations at either dose induced neutralizing antibodies in serum against ancestral SARS-CoV-2 WA1/2020 and several virus variants, although serum titers were lower against the B.1.617.2 (Delta) virus. Protection against weight loss and lung pathology was observed with all high-dose vaccines against all viruses. However, low-dose formulations of the vaccines, which produced lower magnitude antibody and T cell responses, showed breakthrough lung infections with B.1.617.2 and development of pneumonia in K18-hACE2 mice. Thus, in individuals with reduced immunity after mRNA vaccination, breakthrough infection and disease may occur with some SARS-CoV-2 variants.