Do you mean in the years immediately after Pearl Harbor, or ever? Because lots of Truthers today cite conspiracies surrounding Pearl Harbor, although I couldn't quite say when that started.

Edit: It seems that conspiracy theories about Pearl Harbor started floating around as early as 1946

In September 1944, John T. Flynn launched Pearl Harbor revisionism when he published a forty-six page booklet entitled The Truth about Pearl Harbor. Flynn argued that Roosevelt and his cronies had been plotting war against Japan at least since January 1941. The Administration continued needlessly to provoke the Japanese government throughout the rest of the year, and on November 26, 1941, delivered a diplomatic ultimatum that no government could possibly accept. Flynn also suggested that Kimmel and Short were given the wrong instructions from Washington headquarters, thus aborting the taking of effective measures at the base.

In early 1945, a thirty-year-old historian, William L. Neumann, published a brochure, The Genesis of Pearl Harbor. He reviewed the diplomatic background to the outbreak of the war and pointed out how the Roosevelt Administration had launched an economic war against Japan in the summer and fall of 1941. Neumann concluded that both sides were responsible, but that Washington could not have been surprised by the attack at Pearl Harbor, given FDR's diplomatic activities in the months and days preceding December 7th. http://www.ihr.org/jhr/v11/v11p431_Lutton.html

Yes, there were rumors and conspiracies. One popular rumor is that the Americans knew there would be an attack but didn't stop it.