The idea behind it isn't party focused at all. Each state is represented in the House based on population. If, according to the Amendment (and keep in mind when it was written and the reasons behind it), a state acts in a way that denies legal citizens the right to vote, its allocated number of representatives is to be decreased according to the population that was denied the vote. The effect is to then decrease the state's overall say in national governing, with the desired end being that no state would allow voting to be denied, else they lose whatever power they have in the House. This means fewer votes to help push an agenda, to earmark money back to the state, etc.

It's not meant to punish a party, as the House isn't organized to proportionally represent party membership. So, in effect, the amendment wants to ensure that if states deny the vote by N citizens, that they are then recognized as having T citizens (total population) - N citizens (who were denied).