First, let's start with the puzzle "why free speech?". What is the fundamental difference between a legislature forbidding some people from making "indecent" speech at the request of others who fear being offended by such speech, and a legislature taxing some people to pay for other people's education or recreation? In each case interests are opposed, there are political winners and losers, and a majority may trample on some "rights" of a minority. Why should one case be forbidden and the other allowed?
The strongest widely-accepted argument for having courts strike down laws which limit "free speech" is to protect communications intended to influence the political process. You see, even if a large majority preferred to ban indecent speech, or to fund education with taxes, they might never find out that they all preferred this outcome if they were prevented from publicly discussing the issue. Instead, a government might lock in its current advantage and preferences by forbidding any questioning of its current laws. Without free political speech, a minority might much more easily trample on a majority (a worse fate than a majority trampling a minority). Thus political speech deserves extra protection.
Note, however, that this argument for political "speech" applies to any action whose main consequence is to communicate information to influence the political process (and whose other consequences are not overly burdensome to others). So not only should it apply to newspapers, TV, the internet, T-shirts, bumper-stickers, and window signs, but it should also apply to political demonstrations and other expensive political "signals".
You see, the main information communicated by a political demonstration is not the words chanted or held high on posters, but that fact that these people care enough to spend their time demonstrating for this cause. (Thus it is important to demonstrate in clear public view, and to not look like you're having too much fun.) Expensive signals like demonstrations can communicate what mere words cannot - strength of feeling and opinion. (Sure you can say you really care, but everyone says that.)
Unfortunately, many expensive political signals, such as campaign contributions and political advertizing, are widely limited by law. Perhaps such limits can be justified by arguing that these actions can also do much harm, in addition to communicating information to politicians and voters. But I don't see how one can justify the currently wide-spread ban on what I'll call market political signals.
Imagine that we had a market which traded a stock market basket contingent on who became the next president (e.g., trading cash for S&P500 futures, with trades called off if Clinton is not the next president.) The price in this market would constitute a simple easily-understood consensus estimate about which current candidate would be best for the stock market (and be insensitive to who actually wins). Anyone who thought the market price was a bad estimate would expect to make money by trading and helping to correct this estimate.
Since it would be expensive to bet wrong in such a market, the market price would be an expensive signal, aggregating and communicating information not easily found in the "cheap-talk" of media commentary, nor easily disentangled from prices in other markets (if it can be found there at all). In most of the world, however, it would be illegal for you or I to start such a market -- it would be considered illegal gambling or a regulated-out-of-existence security.
Similarly, we might have a variety of "policy markets" estimating the consequences of various political choices. We might have markets in the average sea levels conditional on whether or not a bill limiting CO2 production passed, markets estimating student test scores average and variance conditional on whether school choice programs were implemented, and there might have been markets estimating U.S. employment had NAFTA passed or not.
The primary effect of such markets would be to aggregate and communicate political information. Secondarily, such markets would allow more hedging of political risks, but this is a good thing. So what arguments can there be for banning this political "speech"? Consider standard arguments for forbidding gambling. The markets I propose might make it a bit easier for compulsive gamblers to blow their savings, but given existing financial markets and state-run lotteries, this seems a weak argument. And the paternalistic goal of preventing people from wasting their time and money on unproductive games is hardly relevant to a rule forbidding political participation, which such paternalists are constantly trying to encourage.
Now consider standard arguments for highly-regulated securities, which raises the cost of persuading regulators to allow a new market, and the cost of running such a market, well beyond the means of you or I. Perhaps one could argue that it is more important to protect ordinary investors from con men than to have more kinds of public markets, and that the private markets available only to big businesses (such as one-off derivatives) satisfy most of business's hedging needs.
But the idea of limiting political speech to only big business for fear that ordinary voters might be conned into sending the wrong political signals is not an idea we would accept for any other form of political speech. Could you imagine requiring expensive petitions to regulators who decide which demonstrations or letters-to-the-editor are in the public interest? So why should we accept this idea for market political speech?
To review, the core idea of "free speech" is that efforts to communicate information to influence the political process deserve special protection, because otherwise the current government might prevent a majority of us from realizing we would rather get rid of it. This argument applies not just to "cheap talk" words, but also to any expensive signals which can uniquely communicate strength of opinion, as long as any negative effects beyond that of communicating political information are not too severe.
This argument applies directly and with great strength to policy markets, which would estimate the consequences of political choices. Such markets would have a unique ability to aggregate and communicate information, and seem to have few negative side effects. While efforts to defend indecent speech now may help us prevent a slide down the slippery slope toward state regulation of political speech, a far greater improvement in political information might result from legalizing policy markets.