I wouldn’t expect it would either. A similar type of tax has been put in place in other countries before. The U.S Stock market has so many desirable companies to invest in that I think it would take a much larger tax to see significant declines in investment.
If anything I think it would incentivize people to hold onto stocks a bit longer. High-Frequency traders and brokers would be most impacted and no one is shedding any tears for them.