I'm not sure exactly how much influence the Russians could have on an American Election. The US pretty much looks towards itself when it comes to news, and as for Election Issues, it's an even tighter focus inward. There is, of course, the influence you can get by throwing something out there and letting the victims (American News outlets, US citizens, and the Candidates themselves) do the actual influencing portion, however innocently they come by it.
But any non-US entity really has always had that power, if by some other means than hacking some server somewhere, by raising some issue or acting in some manner that involves a Foreign Policy situation. Still, the US Election is rarely about Foreign Policy issues, at least to the extent that, say, the British Elections traditionally have been. But it seems to me (warning: personal opinion ahead) that broadly speaking an American Presidential Election is about domestic issues, and to a large degree very local issues. In other words, the scope of influence possible with regard to a Foreign Policy issue is I believe small.
If you would argue that even a small influence is too many, well, there is a valid point there, but it seems unavoidable. Looking back, I would say that Israel has probably tried more often than Russia to influence an American election. The net effect was probably greater than zero, but still small, in the grand scheme of things.
Sort of off-topic, but topical, the British Monarchy has a very strict policy whereby no member of the British Royal Family will visit any Commonwealth Nation during an election campaign. By strict I mean to the point where they will cancel any planned visit (and in some countries, they don't get many, so it's a big deal and a big loss) should an election be called. In this case I would suggest it's more a thing of not wanting to be seen to influence an election rather than any actual influence, but there is the argument that a Royal Visit would tend to support the current administration as far as re-election goes.
All in all, though, I think that there are too many issues and too many way in which an Election could potentially be influenced, that in the end you are not going to get much traction from foreign influence in the first place.
Just accusing Russia of an attempt to influence a US Election goes a long way to negating that influence, because the US is somewhat paranoid about foreign influence in the first place (not that it's a rare trait amongst nations, but it does vary and America is on the more, rather than less wary side).
The end result is you can't actually be sure your "influence" is going to go your way; it could easily backfire. The risk itself is probably enough of a brake to make the practice unlikely to be a true influence, versus just one of a thousand small potential influences.