After reading President Trump's full address to the United States Congress on 28 February 2017, I was struck by a particular quote he included:
"abandonment of the protective policy by the American Government [will] produce want and ruin among our people." President Trump was quoting President Abraham Lincoln, who he described as "the first Republican President." What is interesting about this is that both are technically correct, Lincoln did indeed pen that quote, and Lincoln was the first Republican President of the United States. However linking those two made it sound like that quote was representing a policy of President Lincoln in office, and that is not exactly the case.
President Lincoln in the 1860s did support a higher United States tariff, however the quote was taken from his writing on the subject in 1846, when he was about to enter Congress. During his election for the Presidency Lincoln was a great deal more circumspect on the issue of the tariff, due to regional political issues and also the rising tension with the southern states, which remained broadly opposed to tariff protections. More critically though, although the tariff was a means of protecting domestic United States industry at the time, it played a more critical role to the federal government in the early to mid 19th century - mainly as the primary source of revenue for the United States government.
Meet Hiram Barney, the Collector of the Port of New York from 1861 to 1864, President Lincoln's appointee to handle one of the key revenue points in the United States' federal revenue stream. Prior to the legalization of direct income tax one of the key sources of non-borrowing revenue for the United States was tariff revenues, which were broadly collected across all goods imported into the United States. The various tariff bills in the 1850s onward were oriented towards collecting uniform revenues whose purpose was to fund the federal government without favoring one area of the economy over another.
To put it more bluntly, the kind of tariff system designed to generate federal revenue, not to shield the United States economy from foreign competitive trade. Because the economy of the United States in the 1860s was very different than the United States economy of the 1840s, when the quote President Trump is citing was written.
The debate on United States trade policy and the value of tariffs is a fine topic for debate and discussion, economists around the world have varying positions on the subject. But it certainly should not be justified by a quote from 1840s Abraham Lincoln, talking about a fundamentally different way to organize the United States economy and its sources of federal revenue.
Sources: Wikipedia entries on Hiram Barney and U.S. Tariff policy, Abraham Lincoln classroom on Lincoln and the Tariff, the University of Michigan library collected works of Abraham Lincoln (and quote source), and the transcript of President Trump's speech