While the Washington Post and AvWeek have both mentioned the private "space federation" being in mortal fear of regulation overload, neither talked specifics. Finally, this New Scientist article provides the info we need.
In a nutshell, the private-enterprise "space federation" folks don't mind the FAA specifying regulations to ensure their ships don't squash a shopping mall or condo quad. However, what they're desperately trying to avoid is the FAA being put in charge of passenger safety. If that happens, it seems, nobody flies anywhere without the FAA's say-so, and each time something changes the FAA has to come back out and stamp their approval again.
The federation folks would much rather build their own regulatory board. After all, the reasoning goes, if they got into the business of blowing up their passengers they wouldn't be in business very long. It's felt this private self-regulation system would be far more responsive, consistent, and rational than any government agency ever could be. Members of government, predictably enough, disagree, and some are quietly beavering away to ensure they get what they want.
Considering the feds's well-deserved reptutation for arbitrary, irrational, and contradictory regulations, I'm going to side with the business guys right now. The industry is so new, so expensive, and so risky, it almost certainly would just take a single beuracratic bungle to torpedo the entire thing. And we all know just how friendly and quick-thinking the boys in Washington can be.
This is not to say the FAA couldn't do it. They did, after all, shepherd another high-risk, high-cost industry to (eventual) prosperity. But they have enough trouble keeping up with the airline industry, and from the things I have read, the impression I get is they'd just as soon let the companies handle the safety of the passengers in what everyone understands is a very high-risk mode of travel.
The trick is convincing congress not to force the FAA to do it. Which is where the rest of us come in. If you eventually want your own ticket to ride, it's time to ring up your personal congress critter and let them know this is not an industry you want to see hanging from a noose of red tape.