I don't mean to be a jerk, but you're wrong about the Rebuplican Party ever being a "third" party.
The Whig party had already suffered a nearly complete collapse by the time the Republican party was formed in 1854. The Republican party, which had it's roots in the Abolitionist movement, stepped into a huge power vacumn that allowed it to gain immediate traction. Lincoln was only the second presidential canidate nominated by the party when he was elected in 1860.
The difference today, is that neither the Dems or the Pubs are anywhere near collapse and that is what it would take for another party to come into any sort of significance in a national, political sense. Until one of the two parties is abandonded by the vast majority of its constituencies, this is not going to happen, no matter what the Libertarians or Constitution party may dream about their chances; broad public support for them is simply non-existent. Third parties can only act as spoilers, taking votes from the party that most closely shares their ideals.
The Republican party exploded into power out of an intense national debate (slavery) and a wholesale abandonment of the Whig party, but in reality that event was more than 40 years in the making as the Abolitionists' swayed common public opinion in the North against slavery. It was the sort of sea change in public sentiment and view point doesn't happen overnight, but over time. That's the way change takes place a democratic society. Democratic government flows from the opinions and beliefs of the voters. If you want to change Government, you have to change those beliefs. Conservatives have lost ground because we've lost the ability to convince the general public that what we believe is right.
This is why CFR is so damaging. We've lost the institutions that sway public sentiment, and CFR silences us, but not those liberal institutions. Instead of trying to reconstitute the conservative party, we need to be taking the battle to the court of public opinion... the street corners, the press, the churches and temples. We need to be incouraging our conservative young people to pursue careers in journalism. We need to be buying news papers, television stations and networks; in plain speach, we have to get our message out. If we move the public to the right, so goes the government. If we don't, it won't matter because in the end the American people will get what they want.
Please don't get me wrong. I ascripe to the values and beliefs of the Constitution party and to a lesser extent the Libertarians. This country has strayed far from it's Constititional moorings and we've lost precious freedoms, but we've got to play the game by the rules that exist if we don't want to be irrelevant. The primary rule is that you've got to get the majority people to agree with you in the framework of our two party system. In the entire history of our nation, there has never been more than two political parties sharing power and that is not going to change, for better or worse.
God love you