The largest U.S. third parties are:
Largest (voter registration over 100,000)
Constitution Party - Paleoconservatism, paleolibertarianism, Conservative Libertarianism
Green Party - Green politics, eco-socialism, progressivism
Libertarian Party - Libertarianism, laissez-faire
This makes sense- the Greens are far more leftist than the Democrats, yet do not subscribe to socialism (which Americans have a phobia about) or social democracy (which Americans do not know anything about), and the other two parties both cover Americans' minarchist sentiments.
So, what would it take for there to be a Christian democratic movement significant enough to have a major third party in the U.S. alongside these three? (Also, ideas for another thread: what other political ideologies are popular outside of the U.S. that could possibly be imported here? European liberalism is just libertarianism/paleoconservatism, I can't think of any other ideologies, etc.)