So, if they are of the Democratic party, does it not follow they should be called Democratics?
The correct term for a gathered groups is Demagogues.
“a person, esp. an orator or political leader, who gains power and popularity by arousing the emotions, passions, and prejudices of the people.” (Random House Unabridged Dictionary)
How do they refer to themselves? I think they use the word “Democrat”, too. I guess it’s just not OK for Republicans to use it.