I'm not certain access itself is the problem, although the very large availability plays a role. The problem is the toxic culture of gun ownership that spawns a lobby that won't give in a single inch towards any sensible measure. I believe that any sane responsible adult (any citizen, in short) should be allowed to buy and own firearms (all handguns and non automatic rifles at least, won't go into the particular, the line between what's civilian and "military" is an arbitrary one). In return they should submit to background checks, registration, gun education.
2nd amendment is fine. People hell bent on a literal reading of it as if it was a piece of religious doctrine are assholes.