However, once the war began, they viewed slavery as the underlying cause and moved more toward the radicals in favoring the rapid ending of slavery. U.S. Grant may have said it best.
"In all this I can see but the doom of slavery. The North do not want, nor will they want, to interfere with the institution. But they will refuse for all time to give it protection unless the South shall return soon to their allegiance." -
April 19, 1861, in a letter to his father-in-law, Frederick Dent.
I don't think the moral dimension played a part, until Lincoln played it up himself. It was his major message in prosecuting emancipation during the war, and also a plank of his political platform. But I don't think people shared it nearly as strongly.
It took the war, and four years of his use of the bully pulpit in wartime, to drive his message home. I'm sure your Grant quote from April 1861, just as Robert E. Lee was winding up his affairs with the War Department and the U.S. Army, is more typical.
The Virginian antislavery movement withered in the 1820's under the weight of sectional abuse piled atop the calls for abolition from Northern orators. This was a large part of the damage the red-hot Abolitionists did. They made it impossible for Southerners to argue the case themselves, or do anything but close ranks and defend their society.