America is a Democratic Republic. A pure democracy could not work in America, since we are a big nation.
It wouldn't work in any nation. As for "Democratic Republic", I'd be careful when you use those two in conjunction as well. It's the reason Republic has somehow been bastardized into meaning "Democracy". If you're saying that because Republic is representative, well, using Democratic or Representative in front of Republic is about like saying "Man, this is some cold ice", or "This is some hot fire".
"Republic" doesn't need representative in front of it. It is, by very definition, a representative form of government.