Considering that the Republicans rose to replace the Whigs, do you think the Republican Party is a No Homers Party?
We're not discussing the political situation of a century ago, we're talking about the one of today. It is one which has far more modern parallels just in the last few years. They will either split and become a number of smaller parties which are less of a threat or they will be the same party with the same people and the same ideas and simply a different name and no news story about them will neglect to mention that fact.
But they couldn't just change their name and still be the same party; nobody would fall for that, and they wouldn't get their own party to really go along with it anyway.
The name change would probably come from a change of leadership, with the new leadership having a very different ideology (hence the reason I mentioned "Constitutionalist" as a possibility). Existing conservatives would probably cast their lot with this new power bloc just because it would serve as a convenient vehicle for their interests, but it would no longer be defined by the "conservatives" as in the current party. Probably a strain of libertarianish politicians would take the reigns in that case, committed more to legislating individualist philosophies and removing collectivist protections from the Constitution (14th amendment et al) than to anything we might currently recognize as conservativism.
All the same, I would love to see the end of the two-party system in America. Having multiple parties would be good for the country in the long run, but I don't think it's ever going to happen.
But what's missing here is the mechanism by which the leadership implements the change in ideology.
The leadership doesn't "implement" a change in ideology; they simply replace the existing leaders AND their ideology altogether. The case you're describing is basically what happened to the Republican Party during the Goldwater Era; there was a massive sea change with the end of desegregation and a shifting of ideologies. They assimilated the Dixiecrats, synergized their "states rights" ideology (and a fair amount of their segregationist reasoning along with it) and formed the modern Republican Party as we know it today. It's kind of well understood now that the Republican Party of the 1950s bears very little resemblance to its modern incarnation, so much so that they're almost two completely different things.
THAT kind of change wouldn't result in a new party, just the morphing of the existing party into a new form with a new paradigm of behavior, new talking points, new agendas. It's not a new party, but the evolution of an old one.
The arrival of a new party begins with a new set of leaders with a distinct ideology and a distinct agenda. For whatever reason, this new party draws followers to itself (probably because they demonstrate a capacity to win elections more reliably than the existing party) and members of the old party change sides, hoping to cash in on their success. They may or may not subscribe to all (or any) of the ideological goals of the party's leaders, but if they can credibly fake it (or at least uphold some of those ideals to the satisfaction of the party's supporters) then they survive the transition.
The Tea Party types are a passionate and organized group which makes a point of going out to vote and participates in the primary process. This is why they're catered to. If you have a "Constitutionalist" party holding primaries instead, the same groups who are currently going out to vote for Republicans is going to be going out to vote for the Constitutionalists, so you're not going to get a different group of representatives voted in.
Yes you are: the Constitutionalist party has a different set of leaders, which in a democracy like ours pretty much means a totally different set of candidates running (and winning) elections. A few Republicans and Democrats would jump ship and switch parties for whatever reason, but when a new party forms it isn't organized around the same people or the same intellectual background.
This is the reason why the Teabaggers never really split from the Republican party: Tea Party candidates ran in
Republican primaries in an attempt to usurp the positions of candidates they didn't like. That didn't make them a separate political party, jut a sub-group WITHIN the Republican party forming a power bloc. Had the Tea Party stuck with its own primaries and ran in parallel with the Republican and Democratic candidates, they probably would have lost, which is why they didn't do it that way.
These groups also kind of hate the leadership of the GOP and consider them sellouts
But they continue to go along with them despite their gripes to this effect. These groups aren't so much forming a new political party so much as attempting to take control of the old one by replacing its leaders a few at a time and/or pressuring its leaders into adopting their agenda. This, too, isn't the same thing as forming a totally new party.
To be clear: the Tea Party WAS, at first, a new political party, but choosing to remain under the GOP umbrella made this no longer the case. They were assimilated into the body of the Republican Party just like the Dixicrats were, although their influence isn't nearly as transformative.