Depends on your definition of "threat". There was never any danger that the US would ever be invaded or become communist from internal revolution. While communism became the most popular in this country during the Great Depression, it has always been a small minority politically, as has socialism.
But the Soviet Union as a communist empire did seek to expand its control over more countries, exported armed rebellion to achieve this, and even had a branch of government, the COMINTERN or Communist International to pursue this goal. So some countries in Europe became communist, and others were threatened militarily during the Cold War, and when communism began to spread to the Western Hemisphere, Guatemala and Cuba in the 1950s, specifically, we tended to view it as more of a direct threat.
I think it is more accurate to say it was a threat to our resources and economic standard of living as opposed to our very national existence or form of government.
The answer to that question is really a matter of personal opinion. The way it plays out nowadays, it is basically liberal historians who say communism was no threat while conservatives say it was. There is no way to say for sure.
It is definitely true that the Soviet Union had spies in the United States. The spies would surely have done as much damage to the US as they could have. The Soviet Union clearly had enough military power to be a threat, although not enough (by the end of the 1950s) to have a chance to invade the US.
The Soviets clearly wanted to spread communist ideology. However, it is not clear that there was any danger of lots of Americans buying their ideas. Clearly, some politicians did use this threat to help themselves look tough, but that does not necessarily mean it was not a real threat.
So communism was clearly a threat, but there is no clear answer as to whether it was a serious threat.