Not as big as you might think. Looking nation wide for districts that only voted Democrat or only voted Republican, I saw 1041261 Democratic votes and 775970 Republican ones. (I could have missed a district.) If you eliminate those from the tally, we're still around a million excess Democratic votes. And those districts are all going to be very safe for their party, so even if they did have the opposite party as an option, it is likely that most of the votes would have been for the party that won that district.

So that source of skew does not explain much of the difference.