Estadounidense is not a made-up word, it's the correct word for the nationality of someone who comes from the United States.
El presidente estadounidense, Barack Obama, estuve en Guadalajara hace ratito.
Practice the pronunciation till you can say it. You'll sound much more educado (in the Mexican sense) than if you call yourself that other thing.
Obama estuvE aqui?
If you are going to pontificate you might want to avoid beginner's mistakes.
Obama estuvO aqui hace unos dias, (no hace un ratito
We need a rolls eyes smiley on this board.