I messed this up in the first post so let me try again.
If I wanted use the argument Rothbard uses against the possibility of shifting a tax forward, but instead using it against the possibility of shifting a tax backward, I could say:
“It is true that a tax can be shifted backward, in a sense, if the tax causes the demand for the factors of the production of the good to decrease, and therefore the price of the factors to fall on the market. Production in this way is hampered, causing supply to decrease and marginal firms to go out of business. This can hardly be called shifting per se, however, for shifting implies that the tax is passed on with little or no trouble to the producer. If some producers must go out of business in order for the tax to be “shifted,” it is hardly shifting in the proper sense but should be placed in the category of other effects of taxation.”
The reason I think this is applicable is because it seems to me that, firms go out of business regardless of where the tax is shifted, forwards or backwards.