The Republican Party was dominant from 1861 to 1933. The Democratic Party was dominant from 1934 to 1980, the Ghost Party has been dominant ever since. To say this requires accepting many oscillations and digressions between the two non-ghost parties.
What I wish to argue is that there is now a genuine third party of significant size and great volatility. It is really the Independent Party but it refuses to become an official party. The members of this party are registered, in most states, as Democrats or Republicans but they vote their own Ghost Party platform and candidates.
In general the Ghost Party tends to be conservative. The Ghost Party has become more powerful over the past twenty years and has developed its platform due to two key men: Rush Limbaugh who created a vast political radio audience and Rupert Murdoch who created the Fox Network on TV and Cable.
These two men emerged after the American defeat of the USSR and are helping America shape a post-Cold War identity. The identity is part of the Ghost Party platform of: pro commerce, secondary role for government, free trade support, acceptance of a diverse palette of religions and support for America's role as a reluctant global peace keeper.
I think the conservative leaning Ghost Party of independents is here for a long time.