Online voting tools could definitely change the cost as well as the legitimacy of running a superpower scale direct democracy. In Switzerland we largely handle it through voting by letter and every commune handles the counting - technically it's certainly possible to have fraud at that point, however at least I'm not aware of any case where a people's vote would have been faked that way.
Anyway, for larger scale voting I'd have a look at this TED talk: http://www.ted.com/talks/david_bismark_e_voting_without_frau.... E-voting combined with tokens on paper seems to be the winner for me.
But don't forget, the stability of the Swiss system doesn't only come from its direct democratic nature, I'd say the principle of proportionality applied to the government, as I mentioned above, is at least as important. In Switzerland this ensures both checks and balances as well as a government that represents the current political views of the parliament. Also, it lead to a multi-party system with 5 larger players and dynamic coalitions depending on the actual issue. Together with the constant fear of the people's vote this handles most issues quite neatly - even if the process tends to be a bit slower, the output of 'bullshit' is much lower than the things I read from abroad if you will.
The main argument against, as I see it, is the lack of accountability, the prime example being California demanding more spending and lower taxes at the same time. Of course, indirect democracy has done very little to prevent that either.
When Switzerland doesn't pass laws similar to California's, I think it's because they have a much more homogenous society where there is simply a large degree of agreement on how things should be done - and so, the remaining bits lend themselves well to be decided by direct democracy.
That's also my response to the GP: no, no amount of interwebs and technology can turn a large and diverse population that disagrees fundamentally on many important issues into a small and homogenous one that agrees on most things.