The tax would most effect arbitrage trades. Arbitrageurs get between buyers and sellers. When a seller offers a stock for $95 and a buyer is willing to pay $105 the arbitrageurs buy the stock for $95 and sell it to the buyer for a premium (~ $102.5). Arbitrageurs have trading algorithms which can do this millions of times per second, that's how they can buy faster than the "real" buyer. They behave like vultures fighting for the scraps (so to speak) and getting in the way of "real" market participants.
The act of arbitrage trades is taxing market participants already. The proposed tax of ¢3 might make buying stock cheaper on average. (I don't know the real numbers, this is just a guess) Further more I would rather see the money in the hand of the government, as there is a chance that some of the money is spend on better streets & health care. The alternative is to fund hoards of highly skilled engineers to improve algorithm that pick up the scraps. I personally know engineers at broker firms who feel their extremely well paid job provides absolutely no good to society.
EDIT: The main argument for the existence of arbitrageurs is that they provide liquidity to the market when there are not enough buyers & sellers. My personal believe is, they liquidity they provide today comes with a to high of a price. 20 years ago when it was a few guys yelling on the trading floor you could always count on one guy yelling (the arbitrageur). Today the number of market participants & electronic transactions make trades near perfect; The utility of arbitrage trades vanished almost completely.