The main stumbling block to any restriction to gun ownership in American is the NRA.
This group is one of the few places in America where political allegiances, Republican or Democrat, are forgotten in defense of the right granted under the Second Amendment:
Amendment II
A well regulated militia, being necessary to the security of a free state, the right of the people to keep and bear arms, shall not be infringed.
This, in a way, is a similar problem to rigid adherence to the Bible or the Koran, times have changed since the words were written.
The population is now greater by many millions than it was at the time of the Amendment being made, American no longer needs a "well regulated militia", and the laws relating to various aspects of gun ownership have been, like so many others, overtaken and, to a certain extent, sidelined, by the internet.
The Second Amendment is being championed by the NRA depite the fact that the reason that the Amendement was enacted is no longer valid. The money and political power behind the NRA is enormous and, like a lot of other political power, hidden from public view and the will to oppose the NRA is either just not there or is so fragmented as to be useless.