This 1990 Los Angeles Times article quotes military historian Trevor duPuy with the figure of 10,000 expected U.S. casualties, and unnamed officials of the Bush administration, speaking off the record, with estimates of 30,000 Americans.

This article assesses the varying casualty estimates preceding the Gulf War, noting that there was a wide range of estimates but that they were excessively pessimistic almost without exception: it puts partial blame on the use of inaccurate computer models used in war games by the DoD and others, noting that the qualitative analysis put forward by political scientist John Mearshimer in the Chicago Tribune outperformed many others' more quantitative approaches.

This 2002 Brookings Institution paper is mostly focused on projecting casualties for what was then the potential Second Gulf War, but includes some valuable discussion about the reasons behind the weaknesses of those computer models: basically, they were originally designed for projecting casualties in the context of a NATO-Warsaw Pact conflict. Since the Soviets were relatively close to parity with NATO in terms of technology and training, this meant that a certain qualitative parity was baked into the assumptions made by the models when projecting casualty ratios between forces of certain numbers- qualitative parity that did not exist between the United States and Iraqi militaries of 1990.

Quick follow up, is the quote in the show or from the book?