Interestingly, the word "fellow" comes from an Old Norse word meaning a "partner or shareholder of any kind." Once upon a time, when politicians said, "My fellow Americans," they and their audience knew that all of them were shareholders in this greatest of social experiments--representative democracy.
Many other nations have working democracies, in which the citizens get to cast secret ballots, and send representatives to work for them, but only in this country is an entire constitution framed around the notion that all men are created equal, and that different groups can have different interests, but no faction is composed of members who are "more equal" than others. Some men may be richer or poorer, some smarter or dumber, but all have the right to cast one vote, because each owns one share of the democracy.
Now, though, when a politician says, "My fellow Americans," he isn't talking to anyone outside of the room. He isn't talking to anyone who doesn't already agree with him. Sure, politicians say that they operate in big tents, that everyone is welcome, but of course everyone is not.
If we're ever going to become a party that is nationally relevant again in a way that allows us to drive important issues, we have to get back to meaning EVERYONE when we say "my fellow Americans." That doesn't mean that we have to agree with everyone, or to support every faction. We have to figure out how to find what is "American" in those who are pro-choice and anti-abortion; those who are pro-gun and anti-gun; anglican, pentecostal, catholic, muslim, mormon. I'd be interested to know what you think those things are.