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How do high-frequency traders file taxes? Do they list millions of transactions on 10000s of pages to be sent to the IRS?
It depends on how the tax is implemented. Hillary Clinton has said in her financial regulation briefing that her tax would "hit HFT strategies involving excessive levels of order cancellations, which make our markets less stable and less fair." Unfortunately, what most people fail to realize is that high levels of order cancellations are completely normal for HFT firms that engage in market making which is beneficial for all traders. Here is an extremely good article that explains the misunderstanding. Why Do High-Frequency Traders Cancel So Many Orders? If a tax on order cancellations is implemented HFT firms engaging in market making would be disincentivized to complete for the best bid and offer (since this would require them to cancel their previous bids and offers). This would create wider spreads and less liquidity in general. Prices may take longer to adjust as well since firms engaging in various arbitrage strategies would need a greater divergence in price to make the trades profitable. I agree with some other answers that taken to the extreme the US could lose business to other countries with more friendly market regulation.
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I don't think it can get even worse than that. While most of the big players in America have been forced to change or exit the space because of the government, these companies have also been looking for new markets across the world. If we do implement a tax that is too high there would be a backlash from both sides of the aisle. The biggest threat to HFT isn't the US government, and they would only need to raise it one level because of their sheer size as opposed to the current level of the SEC filing. The problem with this argument is that there are other countries that have no regulations on HFT whatsoever.