Derivatives comprise a whole market of different financial instruments. Unlike the commercial banking industry, or the stock market, the derivatives market is "self-regulated" - primarily by the investment banks.
Credit Default Swaps (CDS's) are one segment of the derivatives market (probably making up about 1/15 of the market). Think of CDS's as bets in Las Vegas. There can be winners, losers, and pushes. The CDS market was valued at around $900 million dollars in 2001 (not actual dollars - but the total amount of "bets"). That grew to over $45 Trillion dollars by 2008 (see the problem here...).
A Credit Default Swap is a contract with a buyer and seller. The seller in this case might be an investment bank - and they "sell" asset-backed (could be mortgage) paper to the buyer. The buyer "wins" when the seller defaults, and the buyer gets the spoils.
Now, to make things more complicated - this is an international market and there can by many entities involved in CDS's for a particular tranche (or bucket of money). You have what are know as "counter-parties". These counter-parties can be greatly affected if something "out of the norm" happens to a particular contract.
So, if Paulson rushes in and starts affecting the CDS market you will see an "unwinding" of contracts all of the planet due to the "counter-party" exposure. It will literally implode on itself.
If Paulson doesn't do anything, then the "bets" that are set to go bad will continue to go bad. Liquidity in our market will be gone and we will enter a depression.
Pick your poison - but I opt for the depression because it will be shorter in duration because market forces will "self-cleanse".
That grew to over $45 Trillion dollars by 2008
Good luck to anyone trying to collect.