I was mostly going off my recollections of my high school economics teacher saying something to the effect of "tax on a transaction reduces the market size - for example, tobacco & alcohol duties serve to reduce usage of both products".
Would that not apply for some reason when the product in question is stock trades?
What follows is full of holes but is a mostly correct explanation of what I was talking about before.
Each venue maintains an "order book" for each security that trades on the venue. The order book consists of a number of standing orders, either orders to buy at $k or orders to sell at $j (k<j, with many distinct values of j and k). These orders which sit on the book because they do not have a counterparty are called "add liquidity." When you want to just execute the trade and you don't mind the spread, you place an order that crosses the spread and transact with the person who has the best standing order (selling for the least money or buying for the most money) of all the standing orders. This is called "take liquidity." My impression, which may not be correct, but which forms the basis for my previous response, is that the HFT industry primarily plays the add side right now and that most firms only take liquidity to close out positions when they are unable to close them out by adding liquidity.
The spread is just the difference in prices, it's not an extra fee that some pay and some don't. The only reason it even exists is that where the prices meet trades happen, so the prices never actually meet for long.
It's not that market-makers and HFTs would not be assessed the tax at all, it is that they would be paid more than enough to cover the tax by the people who cross the spread.
This is true if for some reason the HFT wants to take liquidity on both sides of the trade. In reality, the HFT will probably add liquidity on both sides of the trade, making a profit equal to the true spread plus any change in price. Moves of one tenth of a cent will continue to be massively profitable for the HFT, but the HFT's counterparty will have to pay a much larger spread.
One group of people who commonly take liquidity on both sides of the transaction are retail investors, so they would end up taking a great deal of the losses created by this tax.