The obvious alternative to a bailout is letting troubled financial institutions declare bankruptcy. Bankruptcy means that shareholders typically get wiped out and the creditors own the company.
Bankruptcy does not mean the company disappears; it is just owned by someone new (as has occurred with several airlines). Bankruptcy punishes those who took excessive risks while preserving those aspects of a businesses that remain profitable.
In contrast, a bailout transfers enormous wealth from taxpayers to those who knowingly engaged in risky subprime lending. Thus, the bailout encourages companies to take large, imprudent risks and count on getting bailed out by government. This "moral hazard" generates enormous distortions in an economy's allocation of its financial resources.
So what should the government do? Eliminate those policies that generated the current mess. This means, at a general level, abandoning the goal of home ownership independent of ability to pay. This means, in particular, getting rid of Fannie Mae and Freddie Mac, along with policies like the Community Reinvestment Act that pressure banks into subprime lending.
Five years ago, Barney Frank vouched for the "soundness" of Fannie Mae and Freddie Mac, and said "I do not see" any "possibility of serious financial losses to the treasury."
Moreover, he said that the federal government has "probably done too little rather than too much to push them to meet the goals of affordable housing."
Earlier this year, Senator Christopher Dodd praised Fannie Mae and Freddie Mac for "riding to the rescue" when other financial institutions were cutting back on mortgage loans. He too said that they "need to do more" to help subprime borrowers get better loans.
In other words, Congressman Frank and Senator Dodd wanted the government to push financial institutions to lend to people they would not lend to otherwise, because of the risk of default.
This video touches more on the coverup. You will actually here Franklin Raines describe Fannie Mae's assets as "riskless." Not low-risk. Riskless. There's a lot more to the video than just him.
Watch it to the very end, where Bill Clinton makes this remark:
I think that the responsibility that Democrats have may rest more in resisting any efforts by Republicans and the Congress, or by me when I was President, to put some standards and tighten up a little on Fannie May and Freddie Mac.