The conventional wisdom is that eliminating short selling would involve passing new anti-short selling legislation.
Conventional wisdom fails to realize that short selling, as it exists, is largely the contrivance of regulations. For that matter, the procedures on the NASDAQ that allowed unbridled short selling were created by the great Democratic philanthropist Bernie Madoff, former Chair of NASDAQ.
Eliminating naked short selling would be a matter of removing laws.
It would not even require a new bureaucracy. One need simply remove the regulations that allow naked shorting and announce that parties adversely affected by the process can sue the perpetrators of the crime for material damages.
In naked short selling, a person sells property that he does not own. The sell has a direct negative financial impact on the person who owns the property. It is clearly a violation of property rights. Defenders of the practice claim that the naked short seller will have future ownership, and future ownership is equivalent to current ownership. This argument falls apart when one realizes that owership exists in time. The whole investing thing is about buying an equity, holding it through a period of time and selling it again. The investor's hope is that the equity increases in value during that period of time.
Eliminating naked short selling would be a financial deregulation. Eliminating credit default swaps would actually be a deregulation as well. One would simply discard the 11,000 page regulation that made the process legal. This bill was passed in the beginning of the Bush administration (back when Bush was signing his name William Jefferson Clinton).