We develop a new theory relating atmospheric pCO2 and the efficiency of the soft tissue pump of CO2 in the ocean, measured by P*, a quasi-conservative tracer. P* is inversely correlated with preformed phosphate, and its global average represents the fraction of nutrients transported by the export and remineralization of organic material. This view is combined with global conservation constraints for carbon and nutrients leading to a theoretical prediction for the sensitivity of atmospheric pCO2 to changes in globally averaged P*. The theory is supported by sensitivity studies with a more complex, three-dimensional numerical simulations. The numerical experiments suggest that the ocean carbon cycle is unlikely to approach the theoretical limit where globally averaged P* = 1 (complete depletion of preformed phosphate) because the localized dynamics of deep water formation, which may be associated with rapid vertical mixing timescales, preclude the ventilation of strongly nutrient-depleted waters. Hence, in the large volume of the deep waters of the ocean, it is difficult to significantly reduce preformed nutrient (or increase P*) by increasing the efficiency of export production. This mechanism could ultimately control the efficiency of biological pumps in a climate with increased aeolian iron sources to the Southern Ocean. Using these concepts we can reconcile qualitative differences in the response of atmospheric pCO2 to surface nutrient draw down in highly idealized box models and more complex, general circulation models. We suggest that studies of carbon cycle dynamics in regions of deep water formation are the key to understanding the sensitivity of atmospheric pCO2 to biological pumps in the ocean.