We don't. There are no guarantees in this world. Based on what I'm hearing from Wall Street, I'm pretty sure that something bad will happen if we let a whole bunch of banks fail. But I can't promise that everything won't be fine without a bailout. Anyone who promises you that he knows exactly what will happen--whether he is screaming that everything will be fine without a bailout, or that we'll end up back in the 12th century--is both smugly ignorant, and probably trying to sell you something. A distressing number of people commenting on these events seem to believe that we are living in a novel, where the events will unfold with the certainty of a plot contrived by a writer over a long, boozy lunch. The real world is messy. No system that can be outlined in a moderately long book ever works entirely as expected.
We also don't know the bailout will work. We could end up back in the Great Depression anyway. Frankly, we have two data points on massive financial crises that afflict large developed countries which borrow in their own currencies: the Euro-American depression of hte 1930s, and Japan in the 1990s. A lot of what we thought we had learned about dealing with these kinds of crises from the Great Depression failed to stop Japan's decline. What we think we've learned from Japan may turn out not to work on our economy--though, knock wood, hopefully we won't find out. The only surefire way we know of ending such a depression is World War II.
My basic reasoning is this: given just how badly the Great Depression sucked, I'm willing to gamble on stopping it, even if that gamble fails, even if it is not necessary (a question that, if we actually go through with it, will be much argued and never answered). I'm not willing to gamble for the bankers; the worst thing that will happen to them is that they retire on a pittance, or take a boring job somewhere. I'm worried about the 40 million or so people who might end up out of work, and with nowhere to go. I'm willing to do quite a bit to stop that from happening, even let the bankers off scott free. I don't think it's actually necessary to do that, but if I have to choose between helping the 40 million, or expressing my moral outrage--well, there's always skywriting.