WILDLY WRONG: about 5 million
Since that's more than double the total number of deaths per year. The correct answer is 37,000.
About 2,420,000 people die in America each year.
According to the Coalition on Homelessness, the rate of the homeless among those who die is 1,529 per 100,000.
Yielding a total of just over 37,000 per year (this method would show an average of 37,001.8 per year, and obviously by this method you're not going to get an exact count, but a close approximation).