First published on Quora.
This is the system currently used in Maine and Nebraska. In Maine and Nebraska the statewide winner gets the two electoral votes (EVs) that correspond to the senators and then the remaining votes are determined by the winner of each congressional district.
The Electoral College already has a “small state bias” that skews for the time being in favor of the Republicans, since the smaller states tend to be more Republican than the country as a whole. I haven’t checked the numbers, but California has the same population as something like the smallest 20 states combined. That’s two EVs for the statewide win in California compared to forty for the statewide wins in these other states. It’s this bias that is responsible for the two “electoral inversions” we had in 2000 and 2016. That is to say, the two elections where the winner of the Electoral College did not match the winner of the popular vote.
Choosing the remaining EVs by congressional district would further skew things in the Republican direction. This is due to the extreme partisan gerrymander that took place after the 2010 election. To put this into perspective, the Democrats won the “national congressional vote” (NCV) in 2018 by something around 7 percentage points. This will give them a majority of between 14 and 19 seats when the remaining races are determined. By contrast, the Republicans won the 2014 NCV by 5.4 percent in 2014 and that gave them a majority of 30 seats. Worse, in 2012 the Democrats won the NCV by 1.2% but the Republicans maintained a majority in the House of 16 seats.
So, at least until the the congressional districts are redrawn in the wake of the 2020 Census, the current small state bias that favors republicans would be exacerbated. I don’t know if it would be impossible for a Democrat to win the presidency under such a system, but it would certainly be more difficult and there would be many instances where this system would elect the Republican even if the American people preferred the Democrat.
Still, it’s easy to imagine a worse system. During the run-up to the 2012 election, I recall Nebraska debating a return to a winner-take-all system so that President Obama could not win an EV from Nebraska like he did in 2008. At at about the same time the republican-controlled Pennsylvania legislature debated switching to allocating EVs by congressional district to help Governor Romney. Imagine such a system implemented nationwide, with all the red states using winner-take-all and all the blue states allocating by congressional district or vice-versa. Such a system would virtually guarantee one-party control of the presidency.
References (all accessed 19 November 2018):