If you read the correspondence of Secessionist Leaders, at the time of the firing on Fort Sumter, they were afraid that if there wasn’t a war, no further states would secede (the Virginia Convention had already voted to remain in the Union unless war came). Davis thought that without a War of Independence, the states which had seceded would drift back into the Union by shear inertia, since there was a lot of pro-Union sentiment even in the Deep South.
Neither Sam Houston of Texas nor Robert E. Lee of Virginia wanted their states to secede. Their voices carried a lot of weight.