First, why does something need to be done to help those animal-molesting bankers in the first place?
Banks have assets (stuff they own) and liabilities (stuff they owe other people). If their assets are ever worth less than their liabilities, then they're bankrupt and everyone has to clean out their offices by five. Now putting pastry-fucking bankers out of work doesn't sound like such a bad idea these days, but we are talking about some very big banks here, and as I've touched on before, banks do play a pretty important role in keeping the world looking like something other than some of the more incredible scenes from the Road Warrior franchise.
Anyway, many of these banks own toxic mortgage-backed assets (for brevity I'm going to refer to these as 'horseshit' from here on). This horseshit is, amazingly, still considered an asset, although if anyone tried to sell it right now, they wouldn't get a very good price for it, on account of its horseshitty attributes. The central problem here is that some banks own so much of this horseshit that if they valued it at what they could actually sell it for, they would effectively be bankrupt. In short, getting this horseshit off the banks' books without making them bankrupt is our ultimate goal.
This looks pretty impressive until you notice those are ones, and that's maybe 45 bucks there. You've really made it champ.
The government will provide loans for private investors to buy up the aforementioned horseshit from the banks. This would give these banks enough money so they could go about their business and not collapse like an old woman getting out of the bathtub. After that, if the horseshit goes up in price the government gets back their money and splits the profit with the private investors. If the horseshit goes down in price, the private investor takes a small loss, and the government takes a small to enormous loss, depending on various properties of the horseshit (taste? grittiness?)
There's three problems with this plan. One, this involves buying horseshit from the banks for more than it's probably worth, and keeping each bank's current management intact, despite growing evidence that they're colossal fuckers. Two, it involves the private investors taking a chunk of any potential profit while risking only a tiny portion of their own money--effectively another subsidy for wealthy jerks. And the third problem is that this plan may not be big enough. The private investors, even playing mostly with the government's money, might not be willing to pay enough for this horseshit to keep the banks from going bankrupt. So the banks won't sell, and we'll all sit around picking at each other's asses for a bit longer.
The main alternative to this plan is the nationalization of some of the banks. (This has also been referred to as "pre-privatization" or "filthy red socialism" depending on who you talk too.) In this scenario, the government takes over some banks completely. I'm not sure how that works exactly, but I like to think it involves a bureaucrat who looks a bit like Rick Moranis walking in the front door of a bank and firing a gun into the air a couple times to scare everyone off. Once the government owns the bank, they take all the horseshit, transfer it to the government's books, and then resell the bank (intact or in parts) to any private investors who want it. The government can then keep the horseshit or sell it whenever it wants. Temporary nationalizations like this already happen relatively frequently, albeit with much smaller banks.
The big upside to nationalization is the government doesn't have to overpay for anything, nor share any potential profits with the private investors. So ultimately, in this scenario, there should be less cost to the taxpayer. The major downside is taking over and running a bank for a few months or years is potentially a huge headache, and the kind of thing governments routinely screw up. Remember that time the government did that thing really well with a minimum of scandal? Yeah. There's also the worry that nationalizing the banks could turn America into Communist-America, as cautioned by various poorly Xeroxed screenplays that get passed around gun shows and always seem to keep crossing my desk for some reason.
Beyond this, the discussions devolve into a kind of economist pissing match, with arguments about which plan will work best, and why so-and-so is a dullard, and who sucked who off in the men's room of the Olive Garden to get bailout funds. Unsurprisingly, it gets a bit contentious. I'm not going to get into it, but if you're curious, bearded folk have cluttered the Internet with pages upon pages discussing loan modifications and political capital and moral hazard and other things even more boring than this article, if you can believe that.