I suppose that to some people, especially people outside the U.S., it doesn't seem like a big deal. No member of the Democratic Party will object to being called a "Democrat" - but the term "Democrat Party" is always said with disdain. It's a subtle, clever way of creating a negative response whenever people hear the term - just like they've done with the term "liberal."
Does George W. ever refer to the "Democratic Party"? Did Ronald Reagan?

-Joe-