I have an extremely uncomfortable level of cognitive dissonance on this issue, insofar as I don't feel able to say that most of my fellow subjects aren't prepared for direct democracy, but I still suspect I really wouldn't like the country likely to emerge if they were granted it.

I don't have any cognitive dissonance about it. To be for democracy in principle doesn't mean agreeing to any version of it - such as referenda on "initiatives" - as in Calif. Representaive democracy means that in principle there is a group of people voted in to give more detailed consideration to the very complex issues involved in running a large, developed society.

Apart from the average citizen's lack of time or inclination - given the pressures of work, family life, etc., there is the problem of a capitalist system with an inadequate education system, news media geared to making profits rather than spreading enlightenment. So there is a big difference between the potential of one's fellow citzens and the reality of the state of their knowledge and understanding. Cf Chomsky on the issue of potential in relation to sport:

In fact, I have the habit when I'm driving of turning on these radio call-in programs, and it's striking when you hear the ones about sports. They have these groups of sports reporters, or some kind of experts on a panel, and people call in and have discussions with them. First of all, the audience obviously is devoting an enormous amount of time to it all. But the more striking fact is, the callers have a tremendous amount of expertise, they have detailed knowledge of all kinds of things, they carry on these extremely complex discussions...
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Well, in our society we have things that you might use your intelligence on, like politics, but people really can't get involved in them in a very serious way -- so what they do is put their minds to other things, such as sports. You're trained to be obedient; you don't have an interesting job; there's no work around for you that's creative; in the cultural environment you're a passive observer of usually pretty tawdry stuff...So what's left?

Noam Chomsky; Understanding Power, p. 99-100

In relation to serious complex issues like crime, the majority are relatively uninformed and influenced by media exaggerations:

There is a widespread perception that the public are very draconian on law and order: hang `em, flog `em, lock `em up and throw away the key. In one sense they certainly are. Asked in this month's ICM poll if sentences passed by the courts are too soft, too harsh or about right people overwhelmingly think the courts are not handing down harsh enough sentences. 77% think too soft, 18% about right and only 2% too harsh.

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It would appear people don't really think prison works, but at the same time wouldn't want any alternative that would be seen as an easy option. They want harsher alternatives to prisoners, not nicer ones!
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The first question though can also be interpreted though by looking at whether people actually have an accurate perception of what sort of sentences are currently handed down. Unless people work in, or find themselves the subject of the criminal justice system, the only contact they'll really have with sentencing is newspaper outrage about whatever short sentence has been handed down for the latest heinous crime, and that doesn't necessarily give a very balanced view.
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The overall picture though isn't one of the public being wildly more draconian than the actual legal system though - the public would give longer sentences to muggers, thieves and people in possession of child porn and larger fines across the board, but across the board there really isn't a major contrast here between what sentences the public hand down and what sentences judges hand down.

So is the perception that being tough on crime is a vote winner wrong? Not necessarily - people who consider the issue of crime to be important and whose vote may be heavily influenced by crime policy may well be more right wing on the issue than people who really don't care much about crime. Equally, just because demands for harsher sentences may be based upon misconceptions about how tough sentencing currently is, it doesn't make that feeling any less of a driver of opinion.

http://ukpollingreport.co.uk/blog/archives/1022

Although some advocates of direct democracy would have the referendum become the dominant institution of government, in practice and in principle, in almost all cases, the referendum exists solely as a complement to the system of representative democracy, in which most major decisions are made by an elected legislature. An often cited exception is the Swiss canton of Glarus, in which meetings are held on the village lawn to decide on matters of public concern. In most jurisdictions that practice them, referendums are relatively rare occurrences and are restricted to important issues.
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Critics of the referendum argue that voters in a referendum are more likely driven by transient whims than careful deliberation, or that they are not sufficiently informed to make decisions on complicated or technical issues. Voters might furthermore be swayed by strong personalities, or the adverse influence of propaganda or expensive advertising campaigns. James Madison argued that direct democracy is the "tyranny of the majority."

Some opposition to the referendum has arisen from its use by dictators such as Adolf Hitler and Benito Mussolini who, it is argued, used the plebiscite to disguise oppressive policies in a veneer of populism. Hitler's use of the plebiscite is argued as reason why, since World War II, there has been no provision in Germany for the holding of referendums at the federal level.

http://en.wikipedia.org/wiki/Referendum