As long as the private sale channel for guns is untouched, enhanced background checks are meaningless to the overwhelming majority of gun owners. Sure the slippery slope argument is there, but i think enhanced background checks for buying guns from pawnshops, walmart, and online dealers is a good thing. It will prevent a few casual, impulsive buyers who have not had any kind of firearm education from making a bad decision.
The mental health component should bother everyone. This is hard to enforce without trampling our hippa privacy rights. You either need to create a white list for the "sane" or a black list for the "insane". The bar needs to be high. Very high. I could live with people who have been subject to an involuntary committal being put on a mental health black list. This blacklist would need to have a simple removal process. Form from any MD declaring an individual "not seriously mentally ill". Doctors would need to be completely indemnified against liability except in cases of willful negligence in making this declaration.
Gun Ownership at 21 needs to have an easy waiver path too. Take a safety class, get an MD to sign off and you can own a firearm. There are too many legitimate reasons to own a firearm. Hunting, competitive marksmanship, some very rural communities for personal or livestock protection and probate cases where a father might want to leave his firearms to his sons and daughters.
I think this is a pretty reasonable common sense compromise. I would also like to see programs that offer gun safety & training be funded. Give Betsy and the department of defense a billion dollars to expand ROTC programs to offer elective programs in firearm training and safety. It would be a great way to introduce high school seniors to the idea of serving our country and taking advantage of programs like the GI bill. Way more valuable than 2nd rate video games and Super Bowl ads.