I would argue it isn't a losing strategy at all though.
If people start campaigning and supporting a third-party right now, there's actually a shot to win some house seats and local elections next year. That would also be the best time to try, since Repubs have majority of every branch anyways.
After winning local, then they can think senate. Remember that capitalism was only controlled in the 1950s because it feared communism. If you do not pose any threat (even if it is an empty one), they simply will not listen.
TL;DR people are not good with money. There is no point is arguing finances with people that do not know basic math.
So what the conversation devolves to is "stable" vs "experimental" and very few people will choose to be experimental with their health.
The best way to shift favor would be for it to be required to show the cost of insurance on every check (it is currently a hidden fee). This way, when "hooman see big number" removed from gross pay they may reconsider.