Outcomes of presidential elections and the house size, by Michael Neubauer and Joel Zeitlin. (It's in a journal, at PS: Political Science and Politics, Vol. 36, No. 4 (Oct., 2003), pp. 721-725 -- but that's not where I found it, and that's not where the link goes.) The link comes from thirty-thousand.org, a site which claims that congressional districts were never intended to be as large as they are; they advocate one per fifty thousand people, which is six thousand representatives. (Thirty thousand is approximately the original number of people per representative.)
The authors look at the 2000 U. S. presidential election and concluded that given the way in which seats in the House of Representatives are awarded, if the House had 490 members or less the election would have gone to Bush; with 656 or more, it would have gone to Gore; in between it goes back and forth with no obvious pattern, and some ties. The ties come at odd numbers of House members, which surprised me. But the size of the Electoral College is the number of House members, plus the number of Senators (always even, since there are two per state), plus three electoral votes for DC. So an odd number of House members means an even number of electoral votes, as in the current situation where there are 435 in the House and 538 electoral votes.
In case you're wondering why a small House favors Bush and a large house favors Gore, it's because the states that Gore won made up a larger portion of the population, but Bush won more states. In the large-House limit, the number of electoral votes that each state gets is proportional to the population, since the two votes "corresponding to" Senators are essentially negligible. In the small-House limit, each state has 3 electoral votes (I'm assuming that each state has to be represented) and so counting electoral votes amounts to counting states.
The states that Bush won had a total population in the 1990 Census (the relevant one for the 2000 election) of 120,614,084; the states that Gore won, 129,015,599. So 51.68% of the population was in states won by Gore, 48.32% in states won by Bush. Bush won 30 states, Gore 21. (I'm counting DC as a state, which seems reasonable, although the 23rd Amendment says that DC can't have more electors than the least populous state, even though it does have more people than the least populous state.)
So if there are N House members, we expect Bush to win 60 + .4832N electoral votes; the 60 votes are two for each state, the .4832N his proportion of the House. Similarly, Gore expects to win 42 + .5168N electoral votes. (The three are for DC; I'm assuming that DC would always get three electoral votes in this analysis, which isn't quite true. So Bush wins by 18 - .0336N electoral votes, which is positive if N is less than 535. The deviations between this and the truth basically amount to some unpredictable "rounding error".
If you look at the difference between the number of Bush votes and the number of Gore votes, you do see roughly a linear trend. To me it looks like a random walk superimposed on linear motion. This isn't surprising. As we move from N seats to N+1 seats in the House, 51.68% of the time the next seat should go to a Gore state; 48.32% of the time, to a Bush state. (The method that's used allots the seats "in order", i. e. raising N by 1 always adds a seat to a single state. Not all apportionment methods have this property; this is the Alabama paradox.) So the difference between the number of seats in Bush states and in Gore states will fluctuate, but the overall trend is clear. Of course the noise isn't actually random, coming as it does directly from the populations of the states, but the dependence on the state populations is so complicated that we might as well think of it as random.
I believe that something similar would happen with any set of election results in which more states voted for candidate A, but the states that voted for candidate B collectively had greater population. (Note that the latter criterion is not the same as candidate B winning the popular vote.)
Incidentally, I remember hearing in 2000 that if the House had had only a few more seats than it did, or even a few less seats, Gore would have won -- the implication being that N = 435 was a particularly fortuitous choice for the Republicans. This isn't true. But it's also possible that my memory is false.