Op I'm massively anti-gun but you are taking an extremely simplistic view.
As pp's have said the president cannot unilaterally change laws. Any more than David Cameron can (thank god!) see...sometimes that's a good thing, sometimes bad.
America is VAST in landmass alone. The uk can fit several times over into some of the states let alone the entire country, that's before you consider the actual population size difference.
Then there's the fact it's cultural, Americas very existence politically and culturally was as an antithesis to European and later other cultures.
Change this massive takes time, and a lot of money and sadly the gun lobby (catch 22) have loads of money behind them from the sale of...guns! (And ammunition)
'Believe me, it's happening, and it's been happening for a long time. We've been making a lot of noise. There's a very obvious groundswell of support.' This is heartening, I just really hope if god forbid trump is elected, this movement isn't stifled. (Another reason to be terrified of that!) I don't think it's a coincidence that the NRA are right behind him!!
Personally I think one way to quickly greatly reduce the number of guns in America would be high tax payable on each sale (taxing manufacturers would avoid the 'what about street sales' argument). America is a corporation more than a country. Capitalism is king, so make it about money, make it unprofitable.