Severe acute respiratory syndrome coronavirus 2 (SARS-CoV2)-specific neutralizing antibodies (NAbs) lack cross-reactivity between SARS-CoV species and variants and fail to mediate long-term protection against infection. The maintained protection against severe disease and death by vaccination suggests a role for cross-reactive T cells. We generated vaccines containing sequences from the spike or receptor binding domain, the membrane and/or nucleoprotein that induced only T cells, or T cells and NAbs, to understand their individual roles. In three models with homologous or heterologous challenge, high levels of vaccine-induced SARS-CoV-2 NAbs protected against neither infection nor mild histological disease but conferred rapid viral control limiting the histological damage. With no or low levels of NAbs, vaccine-primed T cells, in mice mainly CD8+ T cells, partially controlled viral replication and promoted NAb recall responses. T cells failed to protect against histological damage, presumably because of viral spread and subsequent T cell-mediated killing. Neither vaccine- nor infection-induced NAbs seem to provide long-lasting protective immunity against SARS-CoV-2. Thus, a more realistic approach for universal SARS-CoV-2 vaccines should be to aim for broadly cross-reactive NAbs in combination with long-lasting highly cross-reactive T cells. Long-lived cross-reactive T cells are likely key to prevent severe disease and fatalities during current and future pandemics.