The North Atlantic sediment record suggests quasi‐periodic (7000‐ to 12,000‐year period) ice‐rafted debris (IRD) depositions during at least the last glacial period. The cause of these Heinrich events, as they are commonly known, is not fully understood; however, they may point to surges of the ice stream that drained the Hudson Bay/Hudson Strait region of the Laurentide Ice Sheet. We investigate a simple conceptual model of ice stream instability (the binge/purge model) to suggest ways in which the ice stream could have entrained sufficient debris to account for the estimated mass of IRD associated with a typical Heinrich IRD layer in the North Atlantic (1.0 ± 0.3 × 10¹⁵ kg). We find that freezing of debris‐laden ice at the bed of the ice stream during the brief (≈ 750 years) surge phase of the ice stream's hypothesized binge/purge cycle can incorporate up to 5.1 × 10¹⁵ kg. This amount is sufficient to meet the constraints of the North Atlantic sediment record but by no means verifies the binge/purge model as the cause of Heinrich events.