I saw a presentation at RailsConf two years ago where they took it to the next level. It was the Spanish Internet Party. If they got members in parlament, you could actually vote yourself online, and the MP would just vote based on the constituent votes. You could even delegate your voting power to causes you care about (for example, the EFF or PETA) so that you could have your views represented without having to spend hours or days researching every single issue.
This kind of democracy is what killed Socrates. No, really, the old Athenian system allowed citizens to participate much more directly, so when a moral panic started they could do really nasty stuff.
Now, perhaps I'm being unfair. If you dig a bit deeper, you'll learn that Socrates was officially killed for impiety, and corrupting the young. Unofficially, he was killed for inspiring the Thirty Tyrants. It's debatable whether or not he was in any way responsible for their actions - Plato says no (though Plato was heavily biased) - but it seemed probable to a lot of people at the time. They couldn't get actually punish him for inspiring the Tyrants, because immunity was granted as part of a peace treaty, but when Socrates went ahead preaching his military dictatorship to a whole new generation, people got a bit upset.
Sortition is actually quite a good idea - get a representative bunch of people, and let them debate the issue. It's a jury system. You don't want politicians to decide things, because they are the worst kind of decision makers (or so some people say). You don't want the uninformed populous to make decisions, because they are uniformed. So you get a sample of the populous, let them gather information, and then they can make an informed decision. Sure, Athens did some barbaric shit. But so did practically every other civilization at the time. The only thing to watch out for is people protecting their franchise - Athens stayed quite xenophobic and misogynistic, as the old Athenian men were the only ones who could vote, and didn't want their power being diluted.
It's not either or. After all, isn't spreading the power to many institutions the philosophy behind the American take on democracy.
You could have citizen referendums, give the citizenship veto power (one should probably require more than 50% of the voters for vetoing though). Many other solutions are also possible.
That sounds terrifying really. You'd undoubtedly end up with people only bothering to vote for things they feel really passionately about, which usually falls on the wrong side of rationale.
What's more terrifying - Having no control over what your representatives vote on (except to vote them in or out) or having binding veto power?
Too many people confuse direct democracy with majoritarianism. The same checks and balances that exists with representative democracy can also exist with the direct kind. The constitution & the courts can still limit popular will.
One thing is for sure, there is no way SOPA like bills could pass with direct democracy or popular veto.
