summary: Comparisons of the 1856 and 1860 electoral maps show what Lincoln had to do to win. In 1856, Republican candidate John C. Fremont (red states) did surprisingly well by gathered 114 electoral votes. But Lincoln would need more--152 to be exact.
It was Illinois, Indiana, and Pennsylvania that the Republicans hoped to gain. That would give Lincoln the majority. And as you can see, Lincoln won those states as well as California, Minnesota , and Oregon.
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But it still wasn't easy. No Southern state voted for Lincoln, he wasn't even on the ballot in most of those states. And if the Democratic party has not split and nominated Northern and Southern candidates (Douglas and Breckenridge)--the contest might have been even closer.
Lincoln won with only 40% of the national popular vote. But demographics had really done it for him. The nation was moving North and West and the congressional population numbers, by 1860, had finally gone against the South. For over 70 years, the South had controlled the government because the population had been in their favor. That had now ended.
But instead of accepting their democratic fate, the Southerners decided to leave the Union. This is what the president-elect would have to deal with in March 1861 at his inauguration.