I don’t think anyone believes that the Second Amendment will be repealed or amended, despite what they might hope. The real issue is: Should people have to register to buy a gun and have a background check before buying one?
One fear is that the government will have a list of everyone in the country who owns a gun. This is dangerous information for a government to have. The answer, I think, is to encourage EVERY willing adult citizen to have a background check and receive a license to buy a legal gun (no AK-47s or assault rifles) if he/she passes. The government would then have a list of approved gun owners that would include a majority of Americans. (Convicted felons would be crazy to sign up for a background check, and those with mental health issues who wish to keep them private would most likely not sign up for a background check, either. People with no issues would also be on the list of non-licensed people, so profiling opportunities from this list would be limited.)
If a person doesn’t want a gun, he/she doesn’t have to buy one, despite having a license. Nobody would know whether a licensed person owned a gun, because there would be no requirement to register legal guns when they were purchased. This way, most of the country will be assumed to be armed.
Criminals will think twice about robbing homes and stores. Anyone who doesn’t have a license to carry and is caught carrying would go to jail. Anyone who is caught selling his/her gun to an unlicensed person would go to jail. Anyone who is licensed and who is later convicted of a crime would have his/her license revoked and his/her guns confiscated. And, there should be monetary rewards given to people who report those illegally carrying. Just an idea.
I call this The Penicillin Solution: fighting the problem with the problem.
(The downside is that domestic shootings might increase. I’ll let someone else solve this problem. I don’t need all of the glory.)

Cannon at Fort McHenry (Cannons probably won’t be allowed under The Penicillin Solution, though.)