Two-thirds of both houses have to propose
an amendment, but the President isn't involved. After an amendment is proposed, three-fourths of the states have to ratify it (38 of 50). A handful of Northeastern states might
ratify it (New York, Massachusetts, etc), but that's as far as it would get. The vast majority of states approved concealed carry laws in the last couple of decades, and there's probably more than twelve that recently declared all new federal firearms laws to be null and void in their state, some even tossing in prison time for anyone who tried to enforce them. Just this week a formal recall process started for Colorado legislators who passed their new gun laws restricting magazine capacity, though I doubt they can collect enough signatures given the short time limit.
And a large number of states also have an equivalent of the 2nd Amendment in their state constitutions, sometimes a more detailed and elaborate version. In my state it's unconstitutional to question the constitutionality of the right to keep and bear arms, which is kind of odd.