The earlier Federalist party, for example, supported a stronger Federal government, hence the name. Was there something especially 'Democratic' or 'Republican' that those parties' creators were trying to emphasize?
The federalists always struck me as actually being anti federalist... they were advocating stronger unitary central authority as opposed to federal devolution of authority. It seems to me the democrat republicans where the ones who championed a federalist system with strong states as opposed to the federalist party who really pushed for a stronger centraly government and unitary system.