The President of the United States and the governors of each state have widespread powers available to them to implement gun control policies. As well as federal legislation relating to the ownership of guns, there is also a bewildering array of state legislation in place, ranging from the restrictive, such as in Massachusetts, Hawaii, and New York, to the permissive, such as in Florida, Texas, and Ohio.
In all state constitutions, there is a provision similar to the Second Amendment to the United States Constitution, which relates to the right to bear arms. As with all constitutional provisions, it is wide open to all kinds of interpretations. Hence the radical differences in gun laws from state to state.
In the realm of gun legislation, we see a prime illustration of politics as the art of the possible. Technically speaking, the president as well as all fifty governors could take quite firm, decisive action to restrict the sale and possession of weapons. But in reality, it's not often possible to do so.
For Republican presidents, such as the present incumbent, such action would be politically impossible, given the firm support for Second Amendment rights among members of their party. The National Rifle Association (NRA) was a major financial contributor to Donald Trump's 2016 campaign and looks set to contribute even more money to his reelection campaign later this year.
At the state level, NRA influence is also a very strong factor. But an even stronger one is the fact that tough gun laws are deeply unpopular in some states. If the governor of, say, West Virginia were to propose cracking down on the sale, manufacture, and possession of firearms, then one can be absolutely certain that they wouldn't be governor for much longer. Yes, a governor, just like a president, can show leadership on such a crucial issue; but in most cases, it's difficult to do that without losing office. For most elected officials, political considerations come first, especially so when it comes to gun laws.