Suppose you think centrist, independent voters decide elections. This is the median voter theory of elections. If you believe this theory, then Mitt Romney is the biggest threat to Obama. He is probably a moderate, like the father he hero-worships. He is responsible for Romneycare, the model for Obamacare etc. So, Obama supporters fear Romney as the Republican candidate. They should seek to weaken him as much as possible in the primaries or even try to ensure another candidate is left standing at the end of the primaries.
The strategy of Obama supporters who subscribe to this theory is simple: Give money to Newt Gingrich. He is promising to help Santorum and fight Romney. At worse, he will weaken Romney and at best, given Gingrich’s efforts, Santorum may squeak through.