If you take the "average Joe" who makes 25k a year (which is considerably lower than the median income nationally, btw) and Joe works from the age of 20 until he retires at about 63 - only ever making that 25k, he will have made about the same amount of money as an NFL player who makes the league minimum for the average amount of time NFL players' careers are (3 years). So there would be no need to work two lifetimes.
Any raise, in those 4 decades, would increase the money you make and decrease the time needed to match NFL Player X's income.
Meanwhile, if you make the median income you would only have to work for about 25 years to make as much.
So I don't see how the numbers (generally speaking) support your two-lifetime conclusion for NFL players making the league minimum.