When you say you would vote for a "viable" third party or independent candidate, just what do you mean, exactly?

Among the greatest paradoxes to result from the ideology that sustains the two-party state is the fact that though a majority of the public reject both the Democratic and Republican Parties, refusing to identify themselves with the aims and ends of either, only a small fraction of that same public support third party and independent alternatives to the representatives of the ruling Democratic-Republican political establishment. While browsing the news yesterday for reports on the recent LibDem surge in the UK, I came across a video of John Cleese's "party political broadcast for the Liberal Democrats" from 1997 (via Robert Mackey). In the video, Cleese hones in on this precise paradox, effectively framing it as a constitutive but completely irrational element of the viability hurdle faced by all third party and independent candidates for political office. The comedian states:

People like our policies, so what's the problem? The problem comes because you like our policies. The polls show that half of you prefer LibDem policies and would vote for the Liberal Democrats if you thought we could win. Do you see the problem? Half of you prefer LibDem policies and would vote for the Liberal Democrats if you thought we could win.

That means if you did vote for us, we would win. Right? I mean, not just do well, but actually win. In fact, half the votes would give us the biggest landslide this century. We should be so lucky. So look, when you say that you would vote for us if we could win, I'm not being rude, but what do you mean, exactly?