I do not believe society would accept the installation of an International Criminal Court. The problem with this is the fact that some people are already under more than one jurisdiction, such as citizens of the United States who have to be wary of laws locally, on a state level, and on a federal level. Adding another layer would just cause more problems.
Each country has it's own different rules and regulations that would make the formation of an International Criminal Court to be impossible. Every country has different penalties for different infractions as well as some things are legal in one country than another. This alone would make an ICC impossible to make.
There are so many Federal-level laws throughout the world that any international criminal court would be unable to codify all of them into something that would be universally acceptable; certain acts are acceptable, or condemned, more in various regions throughout the world, and trying to argue that one body should have jurisdiction over all negates the reality of prejudiced judgments based on regional custom.
American citizens probably wouldn't accept an International Criminal Court. Such a concentration of powers would go in the face of American values and beliefs. The court would more than likely have too much power, which is something the American people wouldn't be able to accept. Therefore, it's an unlikely development.
The International Criminal Court is too weak at this point to be accepted by the entire world. If there was one worldwide government, then the ICC would need a large police force to back it up. Plus, its powers must expand to go beyond war crimes for which the ICC is known.