I will define "painter" broadly to include mixed media artists...
To be one of the great American painters, you must satisfy several criteria:
1. You must have an identifiable style and a consistent body of work.
2. Your pictures must complement each other and look better when shown en masse in the form of an exhibit.
3. Your very best pictures must stand among the very best in the American tradition.
4. You must have had a strong influence on other artists, and must capture some essential element of "the American experience."
Let’s start with the nineteenth century today and move on to the twentieth century soon.
Thanks to Paul Keating for posing the question.