I am not sure a vote of non-confidence would have helped here — there are only two parties.
But why are there only two parties?
The rest of the Anglosphere–Australia, Canada, Ireland, New Zealand, the UK–have multiparty systems–some are more multiparty than others, but none of them have the hard two-party system that the US has, in which third parties have a very marginal role (not completely marginal – e.g. in a close election, the decisions of New York's Conservative and Working Families parties can make a real difference to the outcome – but certainly at a national level third parties have no real power in the US.)
First-past-the-post is a popular explanation, but it can't by itself explain it, since the UK and Canada use it, yet lack a US-style hard two party system (and with the rise of the Reform party in the UK, the British system is becoming less two-party than it has been in a long time.)
Just to show up and get 1% of the vote, you would need a grassroots national movement to elect someone who was wildly popular, who could build a 50-state network of volunteers (including legal, political, financial, community organizing, etc), sponsored by someone with extremely deep pockets that doesn't want anything from established political figures. And you'd still lose.
We have representatives already. The problem is we never hold their feet to the fire. We keep voting for the same useless bastards, and we don't vote them out when they do nothing. Half the country doesn't vote. That's our own responsibility we're shirking. Rather than get a new party, we need to get off our collective asses, and use the existing power we have to force the parties to do their jobs.
If I am not mistaken all disruptions to fpp two party systems eventually settle back into them, maybe not the same parties but two nonetheless.
That's overstating it, but it's why the largest group always can form a government. They go to the same aligned parties looking for a majority.
Changing that will require a radical reconsideration of democracy, like replacing FPtP with... something.
Scotland, Wales and Northern Ireland have nationalist movements that want out of the UK-state independence movements exist in the contemporary US too, but they are very fringe
But even England has not just Labor and the Tories, but also the Lib Dems, Reform, the Greens, Restore
So England proves you can have multiple parties with real power, with FPtP, even in the absence of regional-nationalist movements
Point (4) will likely strike many Americans as dubious, but the US doesn't have anything comparable to Québec – there is presently no US state where English isn't the majority language; nor anything comparable to Scotland or Northern Ireland (no state where a significant percentage of its population identify with a competing national identity). So, no matter how much (undeniable) diversity the US has, in the sense that counts for this purpose, it doesn't.
Hence: while abolishing first-past-the-post would no doubt do a lot to break the US hard two-party system, it could also be broken while retaining it if something happened to (2) or (3) or (4) instead.
But, in US politics, changing (2) or (3) is even more politically fringe than changing (1) is. Maybe that might change at some point though, who knows what the future holds.
And (4) will likely eventually cease to be true, but only in the long-run in which we are all already long-dead.