What Stewart Udall meant when he said this is that Cold War weapons programs hurt Americans in the West. These weapons were, of course, meant to threaten the Soviet Union. Instead, Udall says, they harmed people in the Western US. Udall makes these charges (and generally critiques US actions in the Cold War) in The Myths of August.
What Udall is referring to in the quote you mention is the idea that the people who mined the uranium used for the nuclear weapons were harmed by the work they did. Udall cites the fact that Navajo uranium miners in Arizona had excessively high rates of cancer. He says the same of people in a Mormon mining community in Utah. He argues that the US government was willing to endanger the health of these people in the pursuit of its Cold War goals. In doing this, it was aiming to hurt (or at least threaten) the Soviet Union but ended up hurting its own citizens.