Thomas Jefferson's "particular vision" of America was that it should be a country made up of small farmers. Such people would all be relatively independent and self-sufficient and would therefore be good members of a democracy. Jefferson believed that Native Americans could have a part in this vision as well.
Jefferson believed that the Native Americans needed to become like the white people. They needed to give up, or be weaned away from, their primitive ways. They needed to stop roaming the forests as hunters and become farmers like the whites. Jefferson, as can be seen here, wanted the Indians to
either incorporate with us a citizens or the United States, or remove beyond the Mississippi.
Jefferson believed, then, that Native Americans could have a place in American democracy so long as they gave up their traditional ways and became farmers.