'I'm not a Democrat, I'm not a Republican. I Am One Of You. I Am An American. And today I'm announcing my candidacy for the US Presidency. You betcha.' - Sarah Palin, October 2011.
While speculation tends towards whether Palin is going to jump into the GOP race, the more curious question is whether she runs as a third party.
The Republican primary field has very little oxygen left as Bachman and Perry take the position of outsider forcing Palin to either repudiate them or move even more to the extreme right. There's no way she enters the primary unless she feels she can truly win - the loss of the primary on top of her failed VP candidacy would not just close the door to future political aspirations (which we do not know if she harbors) but would kill her commercial/influence value. Furthermore, if she makes if our of the primary, you get Palin v Obama general election. She doesn't win this, even with Obama's sagging poll numbers. Independents push towards Obama, unable at the end of the day to trust Palin in the White House.
But as an insurgent third-party cabinet none of these issues matter. She floats above the primary fray forcing that Republican candidates to beat one another up while Palin campaigns as an independent. A three-way presidential race with Palin as the underdog creates interesting dynamics, depending upon who comes out of the Republican race. If Palin is already known as a third party candidate you're more likely to see someone like Romney emerge given a tea party vote which migrates off of the Republican base and towards Palin. While most mainstream independents split their votes between Obama and Romney. [There's an even stranger scenario where she holds back until GOP chooses Perry and then jumps in.]
Is there any scenario which creates a big enough gap for Palin to squeeze through as a third-party winner? I almost think it doesn't matter -- as a third party candidate Palin increases her influence from outside of the system. A third party candidate is not expected to win the election and so losing to either the Republican or Democrat but gaining a large showing puts her back in play for the next decade. Something that being the second place finisher in a Republican primary or the losing presidential candidate would never deliver.
So basically i can't see a reason for her to jump into the Republican primary but wouldn't be surprised if Palin's camp teases a 3rd party run.