I don't know if I'd say unwinnable, but under the current conditions it's very unlikely that a Republican can win the national popular vote. it's hard to win the popular vote when you're getting blown out in states like California, Illinois, New York, and running close in states like Texas and Florida.
I think you gave the correct analysis. While the GOP is unfairly favored in the Electoral College thanks to the disproportionately many votes of the tiny states, the Democrats have a tremendous advantage for the popular vote thanks to the huge states.
It wasn’t just the big blue (Atlas red) states that gave Hillary the PV. She also wasted her resources in states she didn’t need to win such as AZ, NC, and GA, which pulled these states slightly to the left. This ran up her PV score but was ultimately meaningless in her path to 270. We have no idea what the PV would look like if Hillary strictly focused on MI, WI, PA, and FL. Who knows...if she had hammered on those states and Trump was the one trying to “expand the map,” we may have seen a PV/EV split in the opposite direction.
I seriously doubt that television ads and GOTV operations could have swung the popular vote by 3 million. Those things generally only make a difference with marginal and very low propensity voters, regardless of where they are deployed. Hillary had a built-in advantage in the PV while Trump had a built-in advantage in the EC as a result of the coalitions they had built.
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