Essentially, to fix the financial system, the government had three broad options:
(1) Sit back and do basically nothing, while encouraging the Fed to keep interests rates low. Allow "zombie" banks (those in the red) to borrow money from the Fed at 0 or 0.25%, invest that money in stable assets (e.g. 90-day treasury bonds) and use the spread on those bonds to gradually pay the losses on bad loans. This is the worst option for the economy, and similar to what Japan did in the 1990s. Under that approach, it could take a decade for the banks to recover, prologing the recession and keeping credit tight. People would still suffer, but they couldn't easily point a finger at the government, because they wouldn't have an obvious policy with big numbers to blame. Besides, the zombie banks are still being subsidized at the expense of those wanting to save in the economy (because of low interest rates), its just a blanket subsidy that those without economics/finance background won't notice.
(2) Temporarily nationalize the banks, inspect their books, and forcibly divest them of all the toxic assets. This approach would require the government to somehow value the assets - either by using the current market value (currently about 30 cents on the dollar), or some other method. Stiglitz, Baker, Krugman, and other left-of-center economists prefer this approach, and would like the valuation to be close to the reduced market price, to minimize the potential subsidies to the bank. Sweden used this approach in it's banking crisis, and had good success with it.
--- The upside: This approach also functions as a stress test, telling the government which banks are merely illiquid (don't have enough short-term cash to cover their debt) versus those that are insolvent (have more debt than assets, period). Given the government control of the banks, they could leave the illiquid ones alone, after removing the bad assets, but could use the nationalization to break up the insolvent banks - allowing the risky divisions (e.g. those focused on home lending) to go under, while keeping the profitable divisions as seperate companies. This also reduces the problem of banks that are "too big to fail." Also, if it turns out that the market is underpricing assets (possible, in the current panic), and the government pays less than they're worth, later on the road we make a profit (this has happened before, when the US bailed out Mexico in the mid-90s).
--- The downside: This arguably takes much more up-front government money, because they directly purchase the asset - which makes it a hard sell. Also, if the assets lose value, the government takes a loss (though this can happen under Geithner's plan, too). Lastly, the government might be under pressue from the bankers to overvalue the assets when they buy them - particularly because the public has no idea what they're worth.
(3) Some form of hybrid public-private approach, where the government entices private investors to purchase the bad assets, to remove them from the bank's balance sheets. Essentially, under Geithner's plan, the government creates a restricted market for these assets, by guarenteeing a loan to private investors. So, an investor will put 15% down, borrow the remaining 85% from the government at a low rate, and buy the asset. Also, the investor wouldn't have to pay back the government for the loan, if the asset went bad - so the only loss they would take is their initial investment of 15% of the asset price.
--- The upside: This approach takes less money down. Also, it harnesses the market to do the pricing for the government, requiring less staff time and (again, arguably) potential for screw-up by the government officials. It also (arguably) minimizes the potential losses on the part of the government, because they are simply providing a loan.
--- The downside: The biggest problem is that this "market" is distorted, because the government is subsidizing the purchase of the assets. Investors will be more willing to take risks, overpricing the assets of the banks, and leaving the government to pick up the tab. The higher price asset means that the government may end up spending as much or more money than it would in a simple nationalization plan. Also, the government is not as likely to make money on this plan, because they are loaning investors money at a low fixed rate, in order to buy mortgages that are likely to default. That low rate is likely much less than the potential value of the bad asset if it eventually pays off. After all, why take out a loan if you (the investor) won't profit on the deal? Lastly, the government doesn't have control over the individual banks, however temporarily, so we are likely to be left with the current "megabanks" who - in the event of another bubble - will put us through all of this again.
Hopefully that wasn't too confusing. In any case...
Here are the actual documents distributed by Treasury: http://financialstability.gov/
Here is an interesting op-ed analyzing the potential downfalls of this approach: http://www.guardian.co.uk/
