Abe Lincoln had no high tariff. The tariff in 1860 (before he took office)was significantly lower than it had been in previous years. The Deep South states seceded for reasons that had absolutely nothing to do with tariff rates (until after the war when they were looking around for respectable reasons that would justify secession.)
What absolutely nobody can argue with is that the Deep South states seceded quite some time before Lincoln took office, therefore secession cannot possibly be due to any action of Lincoln.
If you actually read their Ordinances or Resolutions of Secession, they wanted out because of actions or attitudes of northern states or people, not oppression by the federal government. By today's standards, the federal governemtn in 1860 was almost non-existent. It was not oppressive in any logical meaning of the term.
The 14th Congress passed the Tariff Act of 1816 levying a series of 25% duties designed to encourage domestic manufacturingHuh, guess it was over slavery after all. I mean just because the government revenue dropped by over 30 PERCENT that little fort sitting in the middle of Charleston's bay, where interestingly enough tariffs and duties were also enforced, didn't have anything to do with the 'real' reason at all < /sarcasm>Without protective duties, which accounted for an estimated three-fourths of textile manufacturing’s value added, half the New England industrial sector would have gone bankrupt, since European technology produced cloth much more cheaply than American mills could.
In fact, the tariff elevated the rate on manufactured goods to about 50% of their value, resulting in significantly greater protection for New England cloth manufacturers
In July 1832, Congress passed legislation that lowered tariff rates somewhat, but retained the high 1828 rates on manufactured cloth and iron. In November, South Carolina’s special Nullification Convention declared the Tariffs of 1832 and 1828 unconstitutional, and forbade collection of customs duties within the state.
A financial panic induced by a reduction in the flow of British capital investment triggered an extended economic depression, lasting from 1837 to 1843. The Whig Party made its greatest political gains campaigning for more active government programs to stimulate the economy along the model of Henry Clay’s American System. This platform included higher tariffs.
In an electoral sweep, the Whigs gained a congressional majority and won the presidency The party platform endorsed revenue tariffs designed to generate significant funds, part of which were to be distributed to the states to pay for internal improvements (roads and canals), another component of the American System.
Eventually Tyler, too, realized the need for funds, and signed a new bill that maintained some tariffs above 20%, while abandoning revenue distribution
1857--Democrats lowered tariffs further. An economic panic hit soon thereafter, precipitating a fall-off in imports in the wake of the recession that followed. Government revenues plummeted by 30%. In response, the nascent Republican Party called for higher tariffs
For the record quotes are found at Tax.org