Ask stupid questions, you can guarantee you'll get stupid answers. The Pew Research Center polled this question:
WTF? What does that mean? One can take pride in something one achieves through hard work and discipline. Being "an American" is, for almost all of us, a happy accident. (A few people went through hell and immigration snafus to get here; they might be proud of their ingenuity in circumventing obstacles.) We won the human lottery and find ourselves in the richest, if not the sanest or safest, country on earth.
Eighty-three percent of us are "proud" of this. The holdouts, not surprisingly, are younger and browner than the enthusiastic majority.
I could not possibly have answered anything but "Don't Know." The inquiry is meaningless on its face.