From Crossing Wall Street:

Total Democratic Presidential Votes Since 1932: 745,407,082

Total Republican Presidential Votes Since 1932: 745,297,123

Of course, this weighs recent elections, in which more votes were cast, more heavily than older elections. I haven't checked the data, though they link to a spreadsheet with the data, which you folks can easily check if you'd like. Thanks to Prof. Brad Smith for the pointer.