Just because Democrat Senate candidates can win in Republican states does not mean that the GOP does not have a huge natural advantage. If Senate seats were apportioned by population (so California would get 53 and Wyoming 1) and all Senate seats were elected statewide (as they are in the actual Senate), then neither party would have a natural advantage, since Republicans and Democrats are fairly evenly divided in the Electoral College, especially after subtracting 2 EVs from each state. However, since each state elects 2 Senators, and there are a lot more states where Bush won by over 10% (22 of them) than states where Kerry won by over 10% (7 of them), yes, there is a huge natural advantage for the GOP in Senate races. There just happen to be a lot more small states that vote heavily Republican than small states that vote heavily Democrat---16 states with fewer than ten electoral votes gave Bush a 10%+ margin in 2004, while only 3 states with less than ten EVs gave Kerry a 10%+ margin---and thus the equal representation in the Senate helps the GOP.
I understand. We're really playing a word game here. Whatever the size of the natural advantage, it doesn't matter much unless it produces something. Right now, there are 55 Republican senators, several of whom are more like Democrats. And even if all 55 were good Republicans, the difference between 55 and 60 is huge in the Senate. If states voted for senator the same as they vote for president, we would have 60 by now. And we don't, and there is no prospect of it. Would we be much worse off in the Senate if it were proportioned by population? Probably. But that doesn't mean we have a large advantage in practice under the current system. Whether we have a large one theoretically is an interesting topic, but not one with much political significance that I can see. Rats are pretty good at fooling red-state voters, though our people have wised up a bit.