The bailout of F&F should eventually lead to their privatization or disappearance. But that shouldn't be a problem for the housing market. F&F always preached that they served a vital role in the housing industry, making mortgages cheap and housing affordable. Truth is, it's hard to prove that housing would have been less affordable if they never existed. F&F basically performed two functions: 1) they borrowed money in the guise of a government-guaranteed institution at very low interest rates, and then loaned the money to homeowners in the guise of a bank; and 2) they bought loans from lending institutions around the country, then packaged them and sold them to investors, while retaining a lot of the loans on their own books. About the only thing here that was worthwhile was the packaging of loans, but even that is questionable. F&F packaged loans with a guarantee that the investor would never lose principal, which is another way of saying that they would cover any losses that might arise from foreclosures on properties which backed the loans. This was effectively the government guarantee that made F&F MBS so attractive. But there are other ways to do this, the most common being mortgage insurance (PMI). And other institutions could and in fact did package loans and sell them, one being Countrywide. If you remove these institutions from the market, others will step in to take their place. If F&F were to stop buying loans tomorrow, the money they would have had to borrow to buy those loans will be available to buy those loans directly. F&F were just middlemen that used their quasi-government status to borrow too much; when the assets they bought with borrowed money (tons of leverage actually) went south they went bust. It's as simple as that. Now taxpayers have to pick up the pieces because they were so big there is no way the government could let them fail.
For more background, the WSJ has an excellent summary here.