What would happen if the government didn't bail out the banks?

Well not all banks will ''collapse'', capital is afterall fictitious, you'll just get a depression as banks won't be able to give credit since they will have a far more ''real'' approximation of how much money they have to give out. So mortgage payments would spiral while companies cut back or went bust as they could not take loans to cover costs. In the long term you'd get massively lower spending causing further economic contraction leading to a depression lasting years similar to that of 1929. Probably the major worry in the event of a depression is that there may be a run on the dollar, which admittedly is something that does look like it copuld wander into the ''collapse'' scenarios your describing..
I think thats the answer to the question anyways, JK can probably give us a better answer tho.

It's hard to say what would have happened exactly, but it's likely that the credit system in the United States, and consequently in many other countries, would have completely shut down.

To kind of give a little chain of events that occurred in September that scared the shit out of Bernanke and Paulson:

Lehman Brothers (an investment bank) collapsed. It consequently defaulted on its commercial paper, which is the short-term debt that large, generally very safe companies issue to fund their operating expenses (primarily raw materials and wages). This lead a money market mutual fund to "break the buck" (i.e. the current value of its holdings fell below $1/share, so investors had lost money). Since this is a very rare event and money market funds are generally considered extremely safe, this caused a huge panic and a run on the money market funds, which are essentially banks, although though they're not called banks. (You might here the term "shadow banking system" used if you follow economic blogs or the press. Money market funds are one of the main components of this.) The money market funds are major (I think the single largest) buyers of commercial paper. The market for commercial paper consequently dried up and there was almost no lending going on. Even banks were having a hard time getting more than overnight loans, and there were apparently even difficulties with that.

In normal times, the issuers of commercial paper constantly roll over on their debt. (I.e. when payment for comes due, they just issue more paper. They generally don't pay down this debt.) With a sudden contraction of the commercial paper market, enterprises of all sorts (both financial and nonfinancial) would have likely defaulted even though they were mostly solvent. This is because even though they're assets are generally greater than their liabilities, they would've have been able to come up with the cash necessary to settle the immediate claims on them. So they would have been forced into default. This would have scared commercial paper buyers even more (and again, this is generally considered a very safe market), which would have in turn exacerbated the contraction of the commercial paper market, which would have amplified the problems in with the money markets, and so on.

With a complete collapse of the short-term money market all industry would have halted very quickly. This would have very quickly lead to a severe contraction probably far worse than anything seen in the Great Depression.

See this short NPR article, which is a good introduction to the topic: http://www.npr.org/templates/story/story.php?storyId=95099470

If they had let Citibank or Wamu collapse, the problem would have started all over again, probably much worse than with Lehman. It would only be a matter of time (probably not even very much time) before there would have been a run on all banks. I highly doubt even one major US bank would have survived.

So in that specific sense, I think the government interventions have been very successful. The whole credit system would have collapsed months ago if they had just let everything go.

As for your mom's idea that the central bank should just become the main bank, the major central banks have come to act as commercial banks. They have become very significant direct lenders throughout the whole economy. The Federal Reserve now loans to all sorts of enterprises, not just commercial banks (as it does in normal times), and not even just financial enterprises. This is what the central banks always do during times of financial panic. They've even done it for a very long time. I've been reading about the 1856-57 financial panic in Europe and central banks did all these things back then (albeit not nearly on the same scale).

If she's talking about having a major central bank on a more permanent basis (rather than as simply a prop for a failing credit system), then I'd say that I see no reason to believe that a bank created by the state would act any differently than any other private bank once it got into the private lending business. It would have to compete with other banks, either within its own borders or on the world market. Rather than the new state bank transforming the financial system, the financial system would transform the state bank.

There are two really super radio shows from this American Life that give a great run down on the whole thing. Google This American Life and find their radio shows The Giant pool of Money and Another frightening show about the economy. They might want you to pay 95 cents to download, but it's worth it if you want the whole sordid drama laid out from beginning to end.

i don't know much about banking, but why could a state bank not issue resources to projects asking for very low or zero rates of interest on it's investment where it thought necessary?

I'm thinking of the limited initiatives that the government has for social enterprises. Basically what they are doing is introducing new 'social' lending criteria - they want their money back eventually so they can reinvest, but it can be lent for free/at a discount in recognition of the socially beneficial effect of the enterprise.

It could do it, depending on the nature of the banking system as a whole. If the state bank became the sole bank and became the director of industry, you'd have essentially a state capitalist system. Either the nation's industry would compete on the world market or the bank would be little more than tyrannical director of the nation's production.

If we're talking about one state bank alongside the private banks, then the state bank would act more or less like the other banks because of competitive pressures.

There is also a definite tendency for these banks to turn to cronyism. The bank's directors allocate funds to favored clients, friends family, etc.

I don't see how any of this can be construed as beneficial for the working class. The "demand" for nationalization coming from prominent leftists and Marxists (the New Left Review crowd, Leo Pantich, David Harvey, etc.) seems to come from the strange idea that nationalization is inherently beneficial for the working class or equivalent to socialism.

Though I am no economist either, I guess that not bailing out the banks means not bailing out the entire capitalism | state system. The banking system in particular and capitalism in general are based on some sort of confidence–the confidence in the more or less untroubled exploitation of the global working class(es) over a long period of time. I guess the word "credit" in the english language context is quite similar to "confidence", isn't it? Once this confidence disappears, the whole system might propably crash.

Of course not every bank is vital for the system, but even not bailing out a number of small banks might result in crashing bigger ones, because of all them including the national banks are meshed up in a system of re-financing that is very vulnerable to domino effects. The crash of certain banks (mostly the big mortgage banks) might tear down whole states, because the financial strategies and transactions rely on those banks–from nation-wide down to municipal structures. This is why the US and the German government desperately try to stabilize the big mortgage banks. The German government for instance bailed 100.000 million euro only for the HypoRealEstate Bank and it looks as if this weren't enough. Or in other words, if that bank crashes this would result in an extra 1.500 euro debt for every child, man and woman in Germany only for that bail (The other consecuences of a collapse of HypoRealeEstate would propably be much more dramatic). Anyway we must realize that it isn't just "vapor money" that has been burnt in the financial sector within the past few month. It is real money and someone –and this means the working class(es)– will have to pay for it.

As to my understanding, the whole bail out brings us back to the question of confidence. If only some major banks are about to crash, this would crash whole national budgets and get us into a system of hyper-inflation and states of emergency as an attempt of the (then failing) states to get rid of the bails and the social uprising to accompanying the collapse of state and capitalism. I don't know how realistic this scenario is at short term, but it is one option we should prepare ourselves for.

Bankers and their families would go HOURS without food.

Listening to the British bourgeoisie, I think that they were seriously worried that around last October the whole system was about to seize up. This could have meant the freezing of current accounts, no wages paid, no bills paid and so on.
It seems that the bourgeoisie were extremely concerned about this being a real possibility. It wouldn't have been healthy for the working class either.

I would recommend reading the last chapter of Capital on the Accumulation of Capital. It seems to me, whatever we do, the end result will be the same, it's just a matter of how fast it will happen. State-capitalist intervention has been going on for years, and it's main purpose in the US has seemed to be to slow the rate of accumulation while helping the capitalist maximize profits. So we get all the bad things of state-capitalism without the benefits that Canadians and Europeans get, such as universal healthcare, or even proportional voting

If we let the banks collapse, the larger capitalists will accumulate the smaller capitalists, and capital will centralize into fewer banks and fewer hands proportional to the relative population. On the other hand, we see now state-capitalism and international capital struggling for control - will we own the banks, or will the banks own us? That seems to be the real question which will effect our lives greatly in the next few years.