You don't fight terrorism with democracy. You fight it with police tactics and intelligence gathering methods.
Two things undermine democracy faster than anything--the creation of a police state and unrestrained intelligence gathering. So, to say you're going to fight with democracy is another way of saying, "we have no idea what we need to do, but we're going to pretend that civil liberties are important until no one is paying attention."
Civil liberties are the greatest casualty of any terror attack.