Third parties and threatened third party runs keep popping up in American history. The Greens and Libertarians are the biggest small parties just now, but at least have the credibility of some endurance. Other third parties have made bigger splashes in elections, but have then immediately faded. Many, many Americans express dissatisfaction with the two major parties, but somehow, other parties never attract enough voters to become a force.
A semi-independent movement within a party might be more effective. There are already informal factions within the two major parties, but the only one that has current observable power is the Blue Dog Democrats. It makes an intuitive sense, for it combines the best of both worlds: you get most of the benefits of being in a major party, plus some of the benefits of being a separate party.
In the run-up to the Civil War, there were groups such as Independent Democrats, and Democratic-Republicans as well as the Free Soil, Whig, and other entirely separated parties. It was this hybrid nature that led to the eventual realignment that has endured to the present day.
Creating such a subgroup makes a declaration: we Independent Democrats will side with our party in a pinch and for many purposes, but on a few important issues we will go our own way. Such things already happen in Washington, where various caucuses wield influence within their parties, but these identifications exist only informally among the electorate.
I’m a Sorta Republican. A sweet-jesus-those-liberals-are-insane Republican. A Default Republican. As you can see, I’m not very excited by that, but neither am I unhappy. No party is ever going to be quite what you want. If you divide and redivide too much, you become like Brian Jacques’ Guerrilla Shrews. But I might get more excited by a subgroup. You could certainly make a group of Budget Republicans who would by design be de-emphasizing other issues in favor of controlling spending. That might also have more appeal to moderates and independents. Sununu and Gregg were/are clearly Budget Republicans.
I think this works in general, not just for Republicans. For the Democrats, already a more fragmented group, the designations might be a PR loser rather than winner, though.
Are realignments likely to happen any other way?