There is no electoral support amongst "the left," obviously meaning the vast majority of the electorate and the politicians they have put in office, for the government to criminalize misinformation, or eliminate the right for Americans to bear arms.
It's very obvious the "right to bear arms" is not unlimited; you can't buy an Uzi or bazooka from your local gun show and it's not in any way unreasonable to ask if there should be prohibitions on other guns used in mass casualty events.
Personally, I don't think an assault rifle ban fixes the problem since the country is already so awash in guns, but the simple conversation regarding such a ban is not evidence of hating the Constitution or second amendment.
It's just an acknowledgment of how very aberrant the rate of mass shootings in this country are relative to the west of the world, and a good faith conversation regarding how to quell that violence.