I think the Native Americans were there first - just another sorry chapter in British interference with the rest of the world.
To answer more on-topic though, I think nations are better defined by ideologies rather than historic roots - and it's clear that America has shaped it's own (for better or worse). Although we may consider ourselves an older nation, the idea of being "pure British" becomes very problematic considering the number of times we have been invaded and our society radically altered as a result.