First off, this law would be challenged in the courts, so it would likely not be implemented any time soon. But assuming the law were somehow put into place and approved by Congress, it would have a severely negative effect on bitcoin in terms of price and network activity. There would be an underground market, obviously. I suspect most Americans would sell their bitcoin to the government or whoever is willing to buy it. Perhaps seeing the antagonism to bitcoin, China and Russia would consider it an alternative to the U.S. dollar, thus possibly offsetting the impact of American prohibition.

Bitcoin would still be around, however.