Well‐dated sea level records show that the glacioeustatic rise following the last glacial maximum was characterized by two or possibly three brief intervals of rapid sea level rise separating periods with much lower rates. These very high rates of sea level rise indicate periods of exceptionally rapid deglaciation of remaining ice sheets. The Laurentide Ice Sheet is commonly targeted as the source of the first, and largest, of the meltwater pulses (mwp‐IA between ∼14,200 (12,200 14C years B.P.) and 13,700 years ago (11,700 14C years B.P.)). In all oceanic records of deglaciation of the former northern hemisphere ice sheets that we review, only those from the Gulf of Mexico and the Bermuda Rise show evidence of low δ18O values at the time of mwp‐IA, identifying the southern Laurentide Ice Sheet as a potential source for mwp‐IA. We question this source for mwp‐IA, however, because (1) ice sheet models suggest that this sector of the ice sheet contributed only a fraction (<10%) of the sea level needed for mwp‐IA, (2) melting this sector of the ice sheet at the necessary rate to explain mwp‐IA is physically implausible, and (3) ocean models predict a much stronger thermohaline response to the inferred freshwater pulse out of the Mississippi River into the North Atlantic than is recorded. This leaves the Antarctic Ice Sheet as the only other ice sheet capable of delivering enough sea level to explain mwp‐IA, but there are currently no well‐dated high‐resolution records to document this hypothesis. These conclusions suggest that reconstructions of the Laurentide Ice Sheet in the ICE‐4G model, which are constrained to match the sea level record, may be too low for time periods younger than 15,000 years ago. Furthermore, δ18O records from the Gulf of Mexico show variable fluxes of meltwater from the southern margin of the Laurentide Ice Sheet which can be traced to the opening and closing of eastward draining glacial‐lake outlets associated with surging ice sheet behavior. These variable fluxes through eastern outlets were apparently sufficient to affect formation of North Atlantic Deep Water, thus underscoring the sensitivity of this process to changes in freshwater forcing.