What if every single eligible American voted in the presidential election this November?
What are you talking about, large states have the most influence, there's like 4 states that make up over half the votes you need to win. As someone who lives in Alaska, almost never has it been down to whether or not Alaska votes for you. California, New York, Florida, and Texas on the other hand?
I think they meant that individual people in smaller states have more influence than individual people in bigger states
On a technical sense maybe, but again, a state with three votes isn't likely to swing an election. Sure, the ratio of people to electoral votes is lower, but we still only have 3 electoral votes.
The point is that you can win the electoral college without winning the popular vote. About 50% of the population is within like the 10 biggest states. So if the popular vote went 50/50, but they split along the divide of "big states and small states" then the Republicans would probably win about 40 states and would win in a landslide. Even people who support the institution of the electoral college accept this. [Also note it doesn't literally work like that, big states of Texas and Florida seem to be leaning more Republican while small states in New England tend to be more Democratic, but in general this actually lines up pretty well].
This system favors candidates who appeal to more rural states, because you can win more "points".
Anyway, a larger turnout might impact swing states but likely would not affect the winner-take-all result of non-swing states.
Say we have two different scenarios. In scenario 1. We have State X go 49/51 Trump. In Scenario 2. We have the same state go 30/70 Trump-- it does not matter, Trump would get exactly the same number of electoral votes.