The firing on Fort Sumter happened on April 12-13, 1861. Lincoln's call for 75,000 troops was issued April 15, 1875 (75,000). That is not to say that Lincoln didn't have things going on behind the scenes. The Times Picayune (New Orleans) reports the following in the April 11, 1861, edition:
Military Preparations at the NorthThe New York Herald, of the 6th inst., gives accounts of what is going on in this way, in anticipation of a coercive policy on the part of the Washington administration. It says that on the 5th inst., Gov. Curtin, of Pennsylvania, besides being closeted with Lincoln for an hour, had an interview with Secretary Cameron and Gen. Scott, and at 11 o'clock that same night had a private interview with one of Gen. Scott's confidential officers. There is no doubt, it adds, that Pennsylvania will be put upon a war footing immediately.
Massachusetts is said to have six thousand six hundred and seventy men, all equiped and ready to march at twelve hours notice. Among them, says the Herald, are two flying artillery batteries, almost as expert in drill as the best regulars, and several dragoon and cavalry corps, not surpassed in efficiency by any in the volunteer militia in the United States. The infantry troops are well drilled.
New York State, according to the same authority, is pledged to furnish ten thousand men at forty-eight hours notice, and other States in proportion.
I imagine all those pre-Sumter discussions led to the 75,000 figure.
Lincoln was calling out the troops 10 years after he died? Neat trick. But what about the confederate call for 100,000 troops issued by their congress on March 6, 1861?