I read excerpts of the linked article. Such weird, tortuous, and twisted logic I have not read in a long time. Basically what it comes down to is the author is saying, basically, that Jesus would have you vote for those who least support your principles. Let's take that argument ad absurdum. Surely Hillary is a bigger sinner than Guiliani. Why not vote for her instead? Since Jesus preached to sinners, doesn't that mean that he wants you to vote for Hillary?
What standard do we have to judge a candidate, other than choosing that candidate which best represents your views? Most people impose the additional restriction on themselves that they vote for the candidate who best matches their views amongst those candidates with a good chance of winning. But even given that restriction, you vote for the most moral, the most intelligent, the most politically savvy candidate that you can. After all, for better or for worse, the office of President is very powerful. An immoral man will be corrupted by that power. Someone who is not intelligent or politically savvy will be easily manipulated by others. The linked post suggests that we abandon all those standards, and makes the incredible claim that that is what Jesus would have us do.
Modern prophets have suggested that we vote for the most honest, moral person that we can find. I think that is the best guide.

I don't believe anyone needs an appeal to Jesus to prove the point.

Current political reality in America:
1. We have a 2 party system.
2. Liberals vote overwhelmingly for one, conservatives vote overwhelmingly for the other.
3. Most votes for president are quite close 50/50 type of races, give or take 10%

Consequense: When a conservative 3rd party candidate runs, they get their votes mainly from the conservatives. When a liberal 3rd party candidate runs, they get their votes mainly from the liberals.

Basic math: 50/50 or so is good odds, if you force yourself to pick the side in bold and underline.  But when you vote for a third party, your bold underlining looks more like 50 / 30 / 20.  You know what that means?  4 years of President Hillary's grating voice nagging you about being an evil american.  Because (and I can't believe the amount of people that don't want to see this), fifty is more than thirty or twenty!  Yes, there are various strategies or tactics to win electoral votes, and focus on states in different ways.  But guess what - the person with 50% of the people will have these strategies as well, and they'll win.

This is the reality for just about all idealistic 3rd party votes.  Ignoring the reality won't help.  Soapbox whining about how 2 party realists are bad doesn't change the reality.  You wanna 3rd party to win?  You need to do something more than have a viable candidate and a great platform.  You need to have a clear, articulated, persuasive plan on how you will overcome these realities. 

It did work for Lieberman in the last election.  The democrats bumped him and ran some nosepicker who nobody liked.  Lieberman ran as an independant, and most of the republicans and half the democrats voted for him.

Can Thompson or Paul do that?

LM

Who will?

Third parties need to continue to win more local elections to increase their appearance of viability. That will eventually draw main party voters who agree with the positions of the third party, but who want to vote for a winner. But also third parties need to appeal to those voters who have given up on the process in disgust. The main parties won't be picking up those voters anytime soon, since they love to dictate positions to the party members, instead of the other way around. So they're ripe for the picking for third parties.
But, to get to the point, LM is right; if there is a major party candidate who matches your views a little less, but has a better chance of winning, then you should vote for that candidate. Better to get some of what you want than none. But the point that drove me to vote third party (except for the Presidential race, where I will vote for Paul if he gets the Republican nomination) is that there is little to choose between the Democrats and Republicans.
Bush over the past 4 years has increased the size of government, vastly increased spending and taken away personal liberties. That is not the Republican party I joined when I first started voting. If Ron Paul doesn't get the nomination, I see the race as Hillary vs. Hillary Lite, whichever of the remaining pack of Republicans wins the nomination. So LM's argument doesn't sway me in the least. If someone other than Paul gets the nomination, the only difference between whether a democrat or a republican wins the nomination is how quickly the handbasket the country is in will go to hell. That leaves me with only a third party as a choice, since I will get none of what I want whether a democrat or republican is elected, and there's a chance, however slight, that I will get a lot of what I want if a third party candidate is elected.

the only difference between whether a democrat or a republican wins the nomination is how quickly the handbasket the country is in will go to hell

Despite the pessimism toward the eventual state of the country...time seems like a pretty big reason to me.  If voting Rep. delays anarchy or whatever you fear for 5 or 10 years...well, I think that's 5 or 10 years we'll all be glad of.  You know, when the country devolves into tribes and roaming gang rule and all that good stuff that happens to handbaskets.

Well, of course. But voting 3rd party isn't going to do that. Not on national scale.

Nobody yet. Just speculation.