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I hope the vast majority of people would stump up that kind of cash in the absence of any other taxation. If not, I suspect that society is broken in ways that can't be fixed by compulsory taxation, either.To me this is the most interesting line in your reply. There's so much bundled up in here.
First of all; the amount people will pay (and its distribution if they're allowed to nominate policies or departments to fund) would depend entirely on the decision architecture in which their decisions were made.
i.e. Exactly what information is given to citizens and when? What's the nature of their decision? What are the rules and limits? How long is the budget cycle and at what point in the year/month are they making their decision? How are citizens communicated to in the rest of the cycle? What does the broader economy look like after a couple of years of likely-reduced spending? What are the incentives acting on the media and their owners and how does that push them to influence public opinion?
Any mistakes in the implementation of that and it'd be guaranteed to fail (assuming there's any chance of success to begin with).
Secondly, although I think the output of voluntary funding decisions would be mainly a function of decision architecture, that will likely be influenced by overall trends in society. If you read recent work by Robert Putnam you'll probably be aware that the societal indicators of connectedness and social cohesion that he's compiled (things like the % of bipartisan bills, membership of clubs and societies, etc.) have been decreasing from their peak (in around 1964) and are presently on their way down to 1900-era levels. While he doesn't know the cause of that phenomenon, it seems deeply speculative that voluntary tax is the solution.
It's more likely that your desire for voluntary tax is a symptom of your mistrust of others to manage funding decisions for you, i.e. a symptom of the effect he's attempting to understand.