It's difficult to accurately determine a percentage of how many United States citizens may have affiliated themselves or considered themselves communists. Membership peaked in 1947, according to data compiled from the University of Washington at 75,388 members. An actual percentage or number of people affiliated with the ideas of communism is likely impossible to accurately determine as the numbers that the University of Washington gathered is data based on membership to the actual Communist Party. They used statistics from the FBI for the years between 1946 and 1950.
This could potentially cause two problems: What criteria did the FBI consider to be defining one as being a communist? Was it simply showing up to labor meetings? Was it simply showing up to civil rights or labor rights meetings? Simply put, were these numbers inflated by a loose definition of what defined one as a communist?
Further, as a regular citizen during the era of McCarthyism, one could possess communist ideas by association with certain civil liberty groups. McCarthyism and the Red Scare would likely impact lower self-reported numbers of declared involvement in communism. Take Angelo Herndon's piece on "You Cannot Kill the Working Class" and how he was arrested in Georgia on charges of 'insurrection' from an outdated reconstruction era law. The Communist Party's legal arm, the International Legal Defense, represented him and took his case to the U.S. Supreme Court. The labor movement had several groups that either supported communism itself or affiliated themselves with the common goals of the Communist Party at the time. The same applies to the Civil Rights movement and some of its overlaps with communism followers.
So, potentially the best source would be actually reported membership to the Communist Party as attempting to track down numbers for groups that were sympathetic to the movement is likely impossible to accurately measure.
Edit: by mentioning "possessing communist ideas" at the beginning of the second paragraph, I don't mean to imply that civil rights groups or labor groups themselves had communist beliefs. Socially, at the time, some of their beliefs overlapped. One could certainly have been a civil liberty activist without any involvement with the Communist Party. I mean that in a broad context on how the FBI may have viewed it.
sources
https://depts.washington.edu/moves/CP_map-members.shtml
https://www.historyisaweapon.com/defcon1/herndoncannotkill.html
http://content.time.com/time/magazine/article/0,9171,931575,00.html