Having challenged the merits of the goal of taxing only consumption and freeing savings from taxation, we now proceed to deny the very possibility of achieving that goal, i.e., we maintain that a consumption tax will devolve, willy-nilly, into a tax on income and therefore on savings as well. In short, that even if, for the sake of argument, we should want to tax only consumption and not income, we should not be able to do so.... the sales tax is subject to an extra complication: the general assumption that a sales tax can be readily shifted forward to the consumer is totally fallacious. In fact, the sales tax cannot be shifted forward at all!...In the long run, of course, and that run is not very long, the retail firms will not be able to absorb a sales tax; they are not unlimited pools of wealth ready to be confiscated. As the retail firms suffer losses, their demand curves for all intermediate goods, and then for all factors of production, will shift sharply downward, and these declines in demand schedules will be rapidly transmitted to all the ultimate factors of production: labor, land, and interest income. And since all firms tend to earn a uniform interest return determined by social time preference, the incidence of the fall in demand curves will rest rather quickly on the two ultimate factors of production: land and labor.
Hence, the seemingly common-sense view that a retail sales tax will readily be shifted forward to the consumer is totally incorrect. In contrast, the initial impact of the tax will be on the net incomes of retail firms. Their severe losses will lead to a rapid downward shift in demand curves, backward to land and labor, i.e., to wage rates and ground rents. Hence, instead of the retail sales tax being quickly and painlessly shifted forward, it will, in a longer-run, be painfully shifted backward to the incomes of labor and landowners. Once again, an alleged tax on consumption, has been transmuted by the processes of the market into a tax on incomes.
The full Rothbard take on taxes is here.