Cause it wasn't going to be abandoned in 24 hours. Anderson told them that without supplies he would turn over the garrison in a couple days, but Lincoln sent supplies along with a fleet of warships and troops.
Fortunately, Confederate spies saw the warships departing and learned of their destination. The message was relayed to Gen. Beauregard, who in turn sent it to Davis informing them of the impending arrival of Lincoln's fleet. So rather than face a larger, better equipped force that would undoubtedly inflict greater bloodshed in a battle to take the fort, the confederates moved to preempt the fleet's arrival and take the fort.
L. Pope Walker, Montgomery:
Major Anderson has just replied as follows to my summons to evacuate Fort Sumter.
Gen. G. T. Beauregard:Sir -- I have the honor to acknowledge the receipt of your communication, demanding the evacuation of this fort, and to say, in reply thereto, that it is a demand with which I regret that my sense of honor, and of my obligations to my Government prevent my compliance. Thanking you for the fair, manly and courteous terms proposed, and for the high compliment paid me, I am, General, very respectfully, your obedient servant,
[signed] Robert Anderson
Major Anderson adds verbally, I will await the first shot, and if you do not batter us to pieces, we will be starved out in a few days."
Please answer.
[signed] G. T. Beauregard
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Montgomery, April 11, 1863
Gen. Beauregard, Charleston:
Do not desire needlessly to bombard Fort Sumter. If Major Anderson will state the time which, as indicated by him, he will evacuate, and agree in the meantime that he will not use his guns against us, unless ours should be employed against Fort Sumter, you are authorized thus to avoid the effusion of blood.
If this or its equivalent be refused, reduce the fort in the manner you, in your judgment, decide to be most practicable.
[signed] L. Pope Walker
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Charleston, April 11
L. Pope Walker, Montgomery:
Major Anderson will not consent to enter into the engagement you propose. I write you to-day.
[signed] G. T. Beauregard
I don't know what time of day on the 12th that Anderson agreed to this, but the 15th would have been after he would have been resupplied by the Federal force offshore. And the qualifier at the end of his message above makes it seem like he would not evacuate or might possibly open fire if he got supplies or instructions to that effect.
Beauregard had cabled the Montgomery government on the 11th that Anderson had refused his request for an evacuation date and a 'won't fire first' pledge. This was apparently before Anderson's official reply on the 12th above. Again, there is no time of day stated on the Anderson reply. At 3:20 AM on the 12th Beauregard notified Anderson that Fort Sumter would be fired upon in an hour, and at 4:30 the bombardment began.