To start off, this is all hypthetical and does not mean that I believe that it will happen, nor do I hope that it happens. Ok.
The poll numbers that came out yesterday show that Joe Lieberman's re-election hopes to the Senate for 2012 are DOA. If he runs for Senate, he loses. For that reason, he will more than likely decide to retire from the Senate after 24 years of service instead of facing an electorate that wouldn't have him for dog catcher. But what if he's not done?
Lieberman has shown that he wants to be president. He ran for the Democratic nomination in 2004 and McCain toyed with the idea of picking him for VP in 2008. It is highly unlikely that he would attempt to primary the president, as he would have no chance whatsoever of winning. Switching to the GOP and running in their primary would also go nowhere, as the Republican primary electorate is comprised primary ideologues that think Christine O'Donnell make good candidates.
So what's a Joe to do?
President Obama and Joe Biden square off against Jim DeMint and Sarah Palin. The left (obviously) goes to Obama, the right (obviously) goes to DeMint. Lieberman sees his last chance at getting into the White House. He decides to run in the middle as an independent, pulling votes from both the moderate left and the moderate right. His more liberal positions on domestic policy and more conservative foreign policy views could play well with segments of the electorate that think Obama is too far left and DeMint is too far right. He is well known, having been the Democratic VP nominee in 2000 and in national politics for the better part of the past 20, so he would not face the sort of name recognition issues that other "third party" candidates have faced in the past. If he could land some serious fundraisers who are unhappy with the president and the Republican nominee, he could legitimately compete against them. In a serious three-way race, he would only need to pull in 34% of the vote, and even less depending on the strength of other third party candidates.
I'm not saying that this will happen, or that it is even likely to happen. But the presidential election of 2012 could be a lot more like the election of 1992 than people think.