What would adam smith say to a business who wanted tariffs to limit cheap imports entering the country

Adam Smith focused on the role of enlightened self-interest (the "invisible hand") and the role of specialization in promotion the efficiency of capital accumulation. The unobservable market force that helps the demand and supply of goods in a free market to reach equilibrium automatically is the "invisible hand".

Trade statistics were held perceptively and authoritatively to be unreliable (170-1760 aprox.): Heavy duties being imposed upon almost all goods imported, our merchant importers smuggle as much, and make entry of as little as they can. Our merchant exporters, on the contrary, make entry of more than they export; sometimes out of vanity, and to pass for great dealers in goods which pay no duty; and sometimes to gain a bounty or a drawback. Our exports, in consequence of these different frauds, appear upon the customhouse books greatly to overbalance our imports; to the unspeakable comfort of those politicians who measure the national prosperity by what they call the balance of trade.

Hence it is not surprising that Smith, though ready to endorse Gregory King's skill in political arithmetic (I.viii.34), and willing to quote the calculations of Charles Smith on the corn trade (I.xi.g.iS), had to admit that himself had 'no great faith in political arithmetic (IV.v.b.3o) (Adam Smith, 1981, p. 52. "An Inquiry into the Nature and Causes of the Wealth of Nations")

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the tariff was created to protect industry in the northern part of the united states. industries in the north were being driven out of business by imported goods that were priced at a low rate. the goal was to protect these industries   by taxing the goods.