Not long. I am surprised that no one has recognized the fact that the Southron fire-eaters, who were very much in control of the secessionist movement, actually
wanted a war. They didn't care whether the onus of firing the first shot of the war was on them. They had so convinced themselves of Northern weakness and the concept of "one big battle and it'll all be over"-with Foreign Recognition-that IMO short of Union recognition of the CSA the Confederacy was bound to start a fight somewhere eventually.
It was inevitable.
Except that under a weak southern-sympathetic president the South has no reason to secede. See Presidents Fillmore, Pierce, and Buchanan. The Republicans had potentially weak candidates in 1860, but no southern sympathizers. The Republicans were very much a Northern only party. Which is why the South didn't trust them.
The Mexican War was a war of choice led by the South. 3/4ers of the soldiers who fought in that war were Southerners.
a) What could possibly cause a break with a near-Confederate POTUS like Buchanan in the White House?
b) What prevents Buchanan from being impeached (along with his VP) in this scenario? Especially with all those Southern congresscritters going South?
With an earlier secession, Southern Unionists might also be emboldened, however, at what would be seen as much more a "Planter's Revolution".

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No way does the country nominate, much less elect, Benjamin Wade (supporter of women's suffrage!

) or Thaddeus Stevens (Bogeyman #1 for the South, and way too unpopular with too many politicians at the time-a left wing 21st century man living out of his time). Although issuing an Emancipation Proclamation the day that Beauregard fires on Fort Sumter could do as you describe.
To answer your question, it was Buchanan's failure to enforce the Dred Scott decision that could have led to secession. And the Southern states had the best chance of getting the Supreme Court to rule that secession was legal by March to June 1858 when it became apparent that nothing would be done to enforce the Dred Scott Decision, even when it came to Congress recognizing the pro-slavery Lecompton Government in Kansas. The Southern States would be going before the same court that ruled on Dred Scott with no vacancies. I can see a scenario in which the Supreme Court might set a time limit giving Northern states and the federal government 6 months to a year to enact appropriate legislation that would repeal antislavery legislation and if this legislation was not passed, the southern slave states would have the right to secede.
Secession under this circumstance would make it impossible for the North to claim that the South was in rebellion and would maximize public opposition while minimizing public support for war to force the South back into the union.