People who scolded you for using the term "Democrat Senator" are not being paranoid. The fact is that it was an orchestrated attempt by Gingrich in the 1990s to use it to get a subtle negative response to any "Democrat candidate."
BRussell sums it up nicely here:
The most natural phrase would be "Democratic primary" with a large 'D' to distinguish it from a primary that was run in a democratic manner. But many conservative Republicans say "Democrat party." It's almost a litmus test for right-wingedness. Listen to the Limbaughs and other liberal-haters, and they always say "Democrat party" and "Democrat politician" whereas more neutral people or moderate Republicans say the nicer-sounding and more natural "Democratic primary."But of course, the history was really interesting...
Leonard Hall, a former Republican National Chairman, began referring to the 'Democrat' rather than the 'Democratic' party, a habit begun by Thomas E. Dewey. Hall dropped the 'ic,' he said, because 'I think their claims that they represent the great mass of the people, and we don't is just a lot of bunk.'
The University of Virginia's Atcheson L. Hench said of this usage in American Speech magazine: 'Whether they have meant to imply that the party was no longer democratic, or whether they banked on the harsher sound pattern of the new name; whether they wanted to strengthen the impression that they were speaking for a new Republican party by using a new name for the opposition, or whether they had other reasons, the fact remains that ... highly influential speakers ... used the shorter adjective. Some Democrats suggested retaliating by shortening Republican to Publican, but the National Committee overruled them, explaining that Republican 'is the name by which our opponents' product is known and mistrusted."
If you go even further back, apparently you can find Democrats using the term to describe themselves, but that was over 100 years ago, and the Republicans quickly picked it up as a taunt:
In the 1860-1910 period the term was sometimes used by local Democratic parties. In the 1920s the Republicans started using the term, possible to heckle Democrats. Herbert Hoover used the phrase in a campaign speech in 1932: "Many years ago the Democrat party undertook to remedy that whole question of booms and slumps by the creation of the Federal Reserve System." (New York Times, Nov. 5, 1932).
Apparently, though, claim the Gingrich used it based of focus group results is a myth...
Newt Gingrich revived the term "Democrat party" in the early 1990s. Some critics mistakenly believe it is a recent gimmick based on focus groups.
The point remains that only Right wingers and those that listen to right wingers are comfortable with the term "Democrat Party," right?