You can't knock out any one party - it's that bit where if you split the voter bloc of one, the other wins First Past Post.
It is actually possible to knock out both, but we need a national level Social Network Vote Coordination Site to do it. If we can protect it from major sources of inaccuracy, we could do it by the 2016 election to have the Internet Candidate win by write-in. To repeat, if we had a properly secured social site where the entire country announces their intended votes, changing now and then as info surfaces, the big DC politics engine would crumble if they didn't resort to dirty tricks. The results would be: "Republicans, 22% - Democrats 22% - Internet Party 56% FTW and the Lulz".
But it's a big if, because the two big parties have Distraction Odds - they win if we remain too confused to organize it.