While blast effects and lethal doses of radiation (measured in thousands of rem) would affect thousands of people located within a few miles of ground-zero, the threat from cancer-causing radiation doses (as low as 5 rem) would be seen for hundreds of miles and would threaten millions.
We know this because it has already happened. Like reactors, nuclear weapons produce radioactive iodine (RAI), which if inhaled or ingested lodges in the thyroid gland causing cancer and other thyroid damage. It is the primary component of fallout, and its effects were demonstrated by the 1945 atomic bombings in Japan. These effects can still be seen today.
Among Japanese children who were exposed to radiation from the bombings (and who are still alive) nearly half (44.8%) suffer thyroid disease15. Further, atmospheric nuclear weapons testing in the South Pacific and Nevada also spread radioactive fallout causing substantial thyroid damage.
In 1954, for example, unexpected wind effects following the Castle Bravo nuclear test in the Marshall Islands blew fallout onto islands located about 180 miles downwind, exposing children to RAI. Later, a US government study16 found that within 15 years "15 of the 22 Rongelap people who had been under age 10 years at the time of exposure had developed thyroid lesions", and that ultimately "most of the Rongelap children and many adults developed thyroid nodules, some of which proved to be malignant. In addition, thyroid atrophy accounted for severe growth retardation in 2 boys."
Unfortunately, those were not the only victims of RAI. In the US, the National Cancer Institute has calculated that up to 200,000 excess cases of thyroid cancer may have occurred in this country from nuclear weapons testing in Nevada17. Some of these occurred more than 1000 miles away.
Clearly, should a nuclear state or a nuclear terrorist attack the US, the need for KI will be significant.