He was, but I don't see the relevance. What "Republican" and "Democrat" and "Democratic Republicans" and all meant back then has virtually no bearing on what "Republican" and "Democrat" means today. Party philosophies have shifted, who was part of which party has shifted, even which parties were in existence have changed (no Federalists or Whigs anymore).
Jefferson was a Democratic Republican, he founded the party. Does that mean the current Democrats are the Jeffersonian ideal? Do you think many conservatives would agree with that?

I find that factoid to be as relevant as the factoid that Lincoln was a Republican. It just happens to be the same party name...he wasn't a member of the current incarnation of the Republican party.
Really? Are you sure you don't mean that you wouldn't call either party
fiscally conservative? Because that I would definitely agree with. I think the Republicans are much more socially conservative, in that they preach a return to (or defense of) "traditional values" when it comes to what is socially permissible.