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).