Thanks for making something basic in order to put some feedback on it.
1) Colours. Political parties need to have colourful logos in order to attract people.
2) Crown or reverse crown bring your mind to Royalists, we don't want that
3) As Federalist Party is quite liberal, I think a bird would be a good basis where you can invest in
4) A bit more attention of the initials of the party should probably be given too