The ocean has absorbed about 25% of the carbon emitted by humans to date. To better predict how much climate will change, it is critical to understand how this ocean carbon sink will respond to future emissions. Here, we examine the ocean carbon sink response to low emission (SSP1-1.9, SSP1-2.6), intermediate emission (SSP2-4.5, SSP5-3.4-OS), and high emission (SSP5-8.5) scenarios in CMIP6 Earth System Models and in MAGICC7, a reduced-complexity climate carbon system model. From 2020-2100, the trajectory of the global-mean sink approximately parallels the trajectory of anthropogenic emissions. With increasing cumulative emissions during this century (SSP5-8.5 and SSP2-4.5), the cumulative ocean carbon sink absorbs 20%-30% of cumulative emissions since 2015. In scenarios where emissions decline, the ocean absorbs an increasingly large proportion of emissions (up to 120% of cumulative emissions since 2015). Despite similar responses in all models, there remains substantial quantitative spread in estimates of the cumulative sink through 2100 within each scenario, up to 50 PgC in CMIP6 and 120 PgC in the MAGICC7 ensemble. We demonstrate that for all but SSP1-2.6, approximately half of this future spread can be eliminated if model results are adjusted to agree with modern observation-based estimates. Considering the spatial distribution of air-sea CO2 fluxes in CMIP6, we find significant zonal-mean divergence from the suite of newly-available observation-based constraints. We conclude that a significant portion of future ocean carbon sink uncertainty is attributable to modern-day errors in the mean state of air-sea CO2 fluxes, which in turn are associated with model representations of ocean physics and biogeochemistry. Bringing models into agreement with modern observation-based estimates at regional to global scales can substantially reduce uncertainty in future role of the ocean in absorbing anthropogenic CO2 from the atmosphere and mitigating climate change.