The state worker is among millions of immunocompromised Americans, about 3 to 4 percent of the U.S. population, for whom the shots may not work fully, or at all, and who are unsure of their place in a country that is increasingly opening up. Emerging research shows that 15 to 80 percent of those with certain conditions, such as specific blood cancers or who have had organ transplants, are generating few antibodies.