From the Gallup Vault: In December 1938, four German spies living in the United States, some as naturalized U.S. citizens, were found guilty of espionage. It was what the FBI now calls its "first major international spy case." The following month, Gallup found resounding public support for a proposal in Congress to fingerprint and register "all persons living in this country who are not citizens." Seventy-nine percent of U.S. adults agreed with that national security-inspired question.
According to Gallup at the time, "The majority of voters favor the idea because it 'would help to check up on spies,' or would enable the government to 'keep a better line on aliens,' or because it might deter aliens from engaging in crime or other undercover activities." The same Gallup article explained that the minority believed "it would be unfair to 'discriminate against a particular class of people,' or that fingerprinting would be too expensive and would call for 'too much red tape.'"
Notably, in the same poll 67% thought everyone in the U.S. should be fingerprinted.
These data can be found in Gallup Analytics.
Read more from the Gallup Vault.
