Every third-party Presidential run is fundamentally a protest candidacy, trying to make noise and upset applecarts rather than win. The last one to do better than 20% was Teddy Roosevelt in his Bull Moose Party run in 1912.
This doesn’t make sense to me, JC. If one’s aim is to create a third party that will have widespread influence, one needs to find some sort of widespread but unmet political need. And that’s just not going to happen at the local level in a whole bunch of different localities at about the same time. Whatever unmet political needs there are in one place just aren’t going to the same as those that you have two counties over.
State legislatures have a similar problem, just one level up. There are underserved political markets at the state legislature level fairly frequently, but they’ll be very different in Maryland than in Virginia. You can’t build a party out of a whole bunch of differing niche markets.
OTOH, starting off by running a candidate for President may get some attention, but nobody’s really managed to use that as a starting point for building a party.
So what’s left? Congress. And how would you do it? Depends on whether you’re starting a third party of the center or of the extremes.
Personally, I think starting a third party of the center is a waste of time. One decent Presidential run by a centrist candidate usually suffices to get at least one of the two major parties to either moderate its stances, or pretend to, in order to meet the underserved political market and grab those votes. There is never going to be a longstanding opening for a third party in between the other two parties.
So that leaves the extremes. Then comes the question, do you care about the welfare of the party nearer you on the left-right spectrum? IOW, if you’re a left-wing third party, do you want to avoid harming the Dems so much that you put the GOP in power? (Vice-versa for a right-wing third party.)
If the answer is no, you’re free to run Congressional candidates anywhere you want. Just be aware that if you tip some elections the wrong way, you’re going to alienate a bunch of slightly more moderate people who might have otherwise been sympathetic to your cause. That will be a self-limiting factor on the growth of your party. (See Nader, 2000.)
If the answer is yes, then your focus needs to be on ‘safe’ districts - of both parties.
For instance, a left-wing third party would run candidates in districts where it was rare for a Republican to get more than 30%. If you split the left-of-center vote, either you or the Dem wins. No harm, no foul.
And it would run against Republicans in districts where the Dems didn’t run anyone, or where the Dem candidate didn’t have much chance of winning anyway. Why? Because it’s a chance to get your message out, build your party’s brand.
It probably wouldn’t work anyway, for one of several reasons.
One is that you might be imagining the unmet need, kinda the way Broder et al. keep drooling over Unity '08.
Second is that if the need is really there - that is, if the Dems/GOP has moved so far to the center that there’s a whole lot of frustrated voters to their left/right, respectively, you still need good candidates to get your message across, to convince people to vote for your party even in the safest of districts. And good candidates are hard to find, especially when you’re just starting up.
And finally, of course, the major party nearest you may move to co-opt your movement before you get a chance to get very far along with it. If people feel that one of the two major parties is advocating their positions, they’re gonna go with a major party, rather than a third party. That’s just life. If you’re attempting to organize a third party, you need to be prepared to define ‘success’ as pulling one of the major parties closer to where you stand.