I've read this on a several small blogs and in many comments over the last few months: this misguided belief that the Republican party was, at one time, a third party; like the Constitutionist or the Libertarians or the Greens or the Socialist of today.
It's not true. The Republicans were never anything like any of the third parties we have now, because the Republicans were never on the outside looking in at the two-party system. Instead, one of the existing two major parties—the Whigs—collapsed due to an internal schism over the issue of slavery. Then, one of the factions met up and re-named themselves the Republicans. But the people involved were the same people, the same politicians! And a lot of them went straight from being elected Whigs to being elected Republicans!
(Although some of them, fed up with the squabbling, left a few years before the dramatic collapse, and had to be coaxed back later.)
That's completely different then any group of out-of-power citizens trying to build an organization up from the ground floor to challenge the two near-indomitable incumbents. Remember, it is a two-party system. The only road to success for a third party (other than a fundamental voting system change such as approval voting or score voting) is for one of the two major parties to collapse; which has only ever happened in American history because of internal disagreements, never because of an assault from the outside.
So good luck.