That being said, the NFL should pay for this 100%. They should also pay for their stadiums (not threaten local fans / politicians they will move if not being financially supported), and frankly they should pay for any security measures during any NFL games.
The government paying for it is nothing but a quite heavy subsidy they don't need. It's the same though with any big sports league around the world where police / government is handling such affairs and the league is not paying for it.