Ron Suskind's new book describes how Obama wanted to follow the Scandinavian approach to financial crashes by shutting down the banks, wiping out shareholders, and bringing in new management. He charged Geithner with figuring out how to shut down Citigroup. Geithner preferred to ignore his boss's wishes. An earlier book, throws further light on the relationship between Geithner and Citigroup, in which Geithner was offered the job of running Citigroup.
Sorkin, Andrew Ross. 2009. Too Big to Fail: Inside the Battle to Save Wall Street (Allen Lane Penguin Books, London).
61: According to his account of the Lehman crisis, Geithner had been quietly approached in November 2007 by Weill and asked if he would be interested in becoming boss of Citi, a move that could garner him untold millions. Geithner was certainly interested, pondering the matter while on long walks round Larchmont with his dog, Adobe, but a firm offer never materialized.
At that time the credit crisis was really starting to bite, and the giant bank had just reported a record loss. "Weill had no executive function at Citi. He wouldn't be the one making that call if they were seriously interested in giving Geithner the job" points out one banking analyst in commenting on the story. "How else can we interpret this but as a nice juicy carrot being dangled in front of the President of the New York Fed by a bank that was going to need Fed help in a big way."