My humble analysis:
It's interesting to see our reactions to this.
1) influence here is on the impact of what the person did. I don't know that I'd put Lincoln behind Washington, because Washington's desire not to set himself up as life-time leader in the traditional way revolutionary leaders have almost always dones is one of the marks that make him special, and set the tone for one of the reasons why America is different.
But Lincoln is important right up there for keeping America as a union.
Lots of people have done things that are noteworthy, but not all of them had a lot of influence. Sanger is on this list not because of her goodness, but because the birth control movement had a huge impact on the American society, and set the stage for the sexual revolution and the decay of the family in a lot of ways. If that's not influence and impact, I don't know what is.
Harriet Beecher Stowe is on the list because Uncle Tom's Cabin was one of the forces that helped crystalize the final break into the Civil War. Big impact.
Sally Ride (who someone mentioned) is not on the list, because, although what she did was noteworthy, and worth honoring, it hasn't had much impact on what's going on in America.
I still think leaving John Adams off is wrong, because he was the firebrand that kept the unrest fermenting in Boston and helped create the climate that allowed the Revolution to even start. Tom Paine's book without John Adams and his bunch of agitators wouldn't have been enough, IMHO.
LBJ did things we're still dealing with. Big impact, lots of it negative.
As much as I admire RE Lee, and I do, I thought perhaps he was a little high, and I am sure Ben Franklin is too low. Not so sure Babe Ruth had that much impact, but then I might be underplaying the impact sports heros have on society.
Jonathan Edwards definitely had a big impact on how Americans felt and behaved about faith matters, and the approach that would be common in religious movements in America for a long time.
Not so sure about Faulkner being on the list, myself, even though I am a distant cousin of his and I love his work...might be misreading his impact on how we thought about writing, how we thought about ourselves mid-century, how we perceived the South?
It's about legacy, all of this: how did the actions and decisions of the people on the list affect how Americans thought, behaved, acted, and came to be where we are today.
It's by no means all going to be positive.
I'm the one who mentioned adding Sally Ride. The reason is that the women listed were all feminists like Margeret Sanger. I can see adding Susan B. Anthony, but that is about it.
To many women, Sally Ride is a much better example of what the women's movement should be all about. Considering I have 2 young daughters, they know who Sally Ride is, but they have never heard of the other women on the list.
The other woman I would add to the list is Helen Keller. She did become a socialist, but she has probably been one of the most influential persons in our country advocating for people with special needs.
I would rather see Sally Ride, Helen Keller, and Clara Barton on the list instead of Eleanor Roosevelt, Margeret Sanger, Rachel Carson.