When all you've got to hang your hat on is a case from 1903, you say "there are cases that literally go back over a century in support of our position."

If all the other guy has is a case from 1903, you say "they have to go way back in history to find something to support their position."

Couldn't these guys just agree to arm-wrestle to settle this thing?

If, after the recount has been finished, and all challenges have been ruled upon, and the count on the election is less than 133 in favor of either candidate (which seems to be probable at this point), I don’t think the election should be ‘awarded’ to either candidate simply because these 133 ballots were lost.
After all, these 133 people showed up at the polls, voted through a machine, and through no fault of their own, had their ‘receipts’, ie ballots, lost by election officials. Why should this change the result?
How I envy states that have a paper backup in place. Here in PA we don’t even get a receipt when we vote, you push a button and that’s it, no punching, no receipt, no paper spit out, no lights, no sound of the transaction of any kind. I often wondered if I actually voted. I realize that absentee ballots are not usually counted in an election, yet I would prefer to vote this way simply because I could make a physical copy of my vote – something our state doesn’t deem necessary. Everything in Pennsylvania is trusted to an electronic voting machine and count. So, if this election had happened here, it would be over.
Rerunning the election is problematic for multiple reasons. A practical one is the expense and logistics. And, as an election is a snapshot in time, it would be easy to make the argument that a revote would reflect a new choice due to new circumstances and context, especially in that this election would be specifically for the 59th seat in the senate and under an Obama Presidency, something voters couldn’t have explicitly known on November 4th.
Because of this, I would propose the following:
Contact the 133 voters whose ballots have been lost (The machines do record who’s voting, don’t they?). Ask them to sign an affidavit stating whether: a) they voted that day b) the approximate time of day if they voted c) their polling place location. I would not go any further, asking them how they voted would open up a can of worms.
Even if the machines don’t record who voted and there is no way to identify these 133 voters, I would apply the method below. By the way, surveying all registered voters in this particular district would be much more practical and a better reflection of original voter intent on the race than that of re-voting the entire election.
Take the machine count vs. hand recount ratio from the rest of the election and apply it to the machine count on the 133 votes. If, for example, the handcount for Coleman or Franken is 98% of the machine count, multiply .98 times the machine tally on those 133 votes. That should produce a winner. It’s been a long time since algebra class, but I think what we are doing is defining a ‘significant figure’ of victory. If this doesn’t produce a victor, if the margin is just that small, then I say: survey the precinct, revote the entire thing, or have the Senate choose. Since a revote would cost Minnesota money, I would have the revote introduced as a bill in the state legislature. But, applying this method should produce a victor, and, more importantly, a legitimate claim of victory.

These aren't receipts, they are paper ballots. In Illinois we get a "I voted sticker" as a receipt whether we vote electronically or with a paper ballot read by the other faith based machine, the scanner.

The machines do not record who the voter is. It's a secret ballot. I'd say if MN has precedent of counting them the way they were on election night then go with that number. Then ask the Republicans to explain why they don't trust the machines.

Comments about statistics, margins of error, and the like were entirely enlightening and to the point. Nevertheless, it's hard to escape the fact that the eventually the winner in Minnesota will have received in the neighborhood of 1,210,000 votes, give or take four. Two years ago, on the other hand, the winner in Wyoming could have walked away with just 96,289 votes (in fact, the Republican won about 135k to 58k). Whomever Minnesota eventually sends to Washington, he will have received about 12-1/2 times as many votes as his colleague from Wyoming. (Let's not even talk about California!) Once in Washington, however, these differences disappear: both senators get one vote in, say, deciding whether to overcome a filibuster or sustain a veto.

By do means do all countries proceed on this basis versus, say, proportionate representation across the population. The Senate system inevitably--by design--gives disproportionate voting power to (heavily subsidized) farmers. Is there some rationale for continuing to do this, to say nothing of maintaining the filibuster that gives even more power to our country cousins?