How did the Republicans' view of government differ from the Federalists?

The Republicans believed in a strict constructionist view of interpreting the Constitution as written. Is says what it says period. If you don't like it, amend it!

The (Hamiltonian) Federalists believed that the Constitution was a guide that allowed for the "loose-constructionist" view that, so long as something isn't specifically spelled out in the constitution ... well ... it was constitutional (fair game ... legal ... fiat ... the big loophole).