Sunday was the 75th anniversary of Executive Order 9066, which provided the basis for sending people of Japanese ancestry (and some of German or Italian ancestry) to internment camps. As far as I can tell, no contemporary survey asked people whether they agreed with the policy. In December 1942, a Gallup poll asked "Do you think the Japanese who were moved inland from the Pacific coast should be allowed to return to the Pacific coast when the war is over?" 35% said yes, 48% no, and 15% weren't sure. There was also a follow-up "Should American born Japanese be allowed to return to their homes on the coast after the war?" and about 23% gave a combination of no or not sure on the first and yes on the second.*
In 1946, a NORC survey asked "do you think the average Japanese person who lives in this country is loyal or disloyal to the American government?" 50% said loyal, 25% disloyal, and 25% didn't know. People who said "loyal" or "don't know" were asked "do you think the average Japanese person now living in this country who is not a citizen should or should not be allowed to become a citizen?" Combining the two, 42% said should be allowed to apply for citizenship, 21% sail loyal but should not, and 25% said disloyal (and presumably should not), and the rest not sure about loyalty and whether they should be allowed to apply.
In 1991, a Gallup poll asked " Here in this country, the U.S. (United States) government required many U.S. citizens of Japanese descent to leave their homes and move to relocation camps during World War II. Looking back, would you say you approve or disapprove of this action?" 33% said they approved and 62% disapproved.
The 1942 survey didn't ask about education, but the 1946 and 1991 surveys did. In both cases, it was associated with more sympathetic attitudes towards Japanese-Americans. In 1991, 36% of people without a high school diploma said they approved and 50% disapproved; among college graduates it was 22% approve and 75% disapprove.
One way to look at this comparison is that it shows that there was probably a change in public opinion. The fact that the Gallup poll didn't even ask about general approval of the order suggests that they didn't think it was controversial. Also, at that time they frequently classified and recorded answers that didn't fit into the standard categories: they counted 1% as giving what they called "yes, if" answers, but didn't record anyone as saying something along the lines of "they never should have been moved in the first place." in 1991, a clear majority disapproved. Another way to look at it is that something that was universally condemned among political and legal elites by 1991 still had significant support in the general public.
*Some of the "don't knows" weren't asked the follow-up: if they had, it would probably have been up to 25% or 26%.