I have been comfortable calling myself a socialist for several decades now. Not in the Karl Marx type of socialism, but in the "social democrat" type system exemplified by the Nordic countries in Europe -- countries that regulate their capitalism to protect workers and consumers while helping their most unfortunate citizens with a social welfare system.
And I believe that is true of most "progressives" in the Democratic Party -- and even of Independent Bernie Sanders (who calls himself a socialist). These people don't want to see all private property or private businesses eliminated. They just want a system that is fair to all citizens -- providing opportunity, equality, and meeting the basic needs.
But the Republicans would like to brand all Democrats as socialists. They know that most Americans don't understand what socialism really is, and want to take advantage of the misconceptions many Americans have about it (the idea that it equates to communism or dictatorship). It's not true, but it might work.
Note the chart above. It reflects the results of the latest NBC News / Wall Street Journal Poll -- done between February 24th and 27th of a national sample of 900 adults, with a margin of error of 3.27 points.
Only 25% said they would be comfortable voting for a candidate they viewed as a socialist, while a whopping 72% said they would not be comfortable voting for that candidate. That's the lowest percentage of any of the qualities listed in the chart.
Some progressives think they can educate the public about socialism, and change their opinion. I think that is wishful thinking. Anti-socialism propaganda has been strong for many decades in the United States, and it's going to take more than one election season to change those views. It would be a mistake for any Democratic candidate to embrace the term, or to let Republicans brand them with it.