Republicans are fond of calling the Democratic Party the Democrat Party. The reason is clear (and spelled out here). It is a way for them to avoid using the patriotic imagery that "democratic" implies, plus it sounds harsh, and--bonus!!!--irritates members of the party.
Many prominent Republican politicians, and nearly all right-wing talk radio and cable news blow-holes use the incorrect term. And while I have no problem believing that Sean Hannity might be too stupid to know he's using it wrong, I'm quite sure that most of them do. The galling thing is when these people and their defenders deny that it's on purpose. In fact, in the link above you'll find one of them digging for places where more liberal people have misused the term. It's like the insistence that FOX "News" is fair and balanced and not right-leaning. . .even though almost all FOX defenders are right-wingers.
Anyway, a member of the House of Representatives, Marcy Kaptur (D-Ohio) finally called out one of her colleagues for saying "Democrat Party" repeatedly. It's about time.