The 'American way of life', as uttered by the President in various nationalism-rousing speeches (or speech impediments), is, I believe, a reference to democracy and the belief in freedom, truth, justice, equality, and all the other things that look good on paper but no government actually practises. It is an ideal that people believe in whether or not it actually exists, and thus don't have to ask themselves if it does.
A more cynical interpretation would be to consume and destroy, the MO of most western civilisations. As a mantra, it is far less appealing.