So the fact that the US had the atomic bomb was totally secret prior to its use on Hiroshima. So there would have been no public protest before their use, for that reason alone, even if there was public opposition.

But there was not public opposition after their use. An October 1945 survey of Americans found 85% in favor of the use of the atomic bombs, only 10% opposed. A Forbes poll from November 1945 found that only 4.5% of Americans believed they shouldn't have used the bombs at all, only 13.8% believed that the bomb should have been demonstrated on an uninhabited area first, and a whopping 53.5% were happy with them being used exactly as they were, on two cities. And, tellingly, 22.7% expressed the wish that "We should have quickly used many more of them before Japan had a chance." (Any missing percentage points in the above surveys are people who had no response/did not know.)

Which is just to say: the US was very much in favor of the use of the atomic bombs in 1945. One can attribute this to a number of factors, including the idea that they "ended the war" (we have no surveys about their use prior to Japan's surrender, unfortunately), as well as bitterness regarding the Japanese (Pearl Harbor, treatment of Allied POWs and occupied countries, overt racism, etc.), and an official narrative that presented the atomic bombs as the result of careful deliberation and as the only alternative to invasion. But the underlying theme is that while Americans were at times ambivalent about the invention of the atomic bomb — because they saw that it could lead to a more dangerous world — they were as unanimous as you can essentially get in 1945 that the bombs ought to have been dropped on Japan.

Opinion on nuclear arms did change over the next decades, and there were large public protests in the 1960s, 1970s, and 1980s. But I read your question as being about the use of the bombs in 1945, not the later decades.

The survey data cited comes from Hazel Gaudet Erskine, "The Polls: Atomic Weapons and Nuclear Energy," Public Opinion Quarterly 27, no. 2 (Summer 1963), 155-190. For a good history of the later anti-nuclear movement, see Lawrence Wittner, Confronting the Bomb: A Short History of the Nuclear Disarmament Movement.