To add a little to what Frank said, one of the primary differences between the 1A and the 2A is that the 1A has been the subject of literally dozens of Supreme Court cases stretching back for many decades, so lawmakers have a clear idea of where the limits are- i.e. they have clear guidelines on how to write a law that's likely to survive a court challenge.
OTOH the number of important Supreme Court cases concerning the 2A can, believe it or not, be counted without running out of fingers, and the most crucial ones are less than 5 years old! Furthermore, although Heller
are largely considered victories for the RKBA, they do not slam the door on all
regulations. There are also a number of ambiguities in the decisions.
We can expect gun control advocates to push severe regulations in an attempt to learn where the limits are. Many of the new regulations are unlikely to survive in court, but they will result in discomfort for many law-abiding gun owners in the interim.