It was their cause, I would expect them to put personal effort into it. And not all Southerners agreed with slavery, me being one. But it is the politicians who rule the roost until the day citizens get fed up and act like employers instead of slaves themselves!
Indeed, nearly every Confederate state supplied troops for the Union Army.
You may know, historians usually divide "the South" into three major regions: 1) Deep South -- seven original Confederate States, 2) Upper South -- four states which joined the Confederacy after Fort Sumter, and 3) Southern Border States -- four slave states which never voted to secede.
I think it's fair to say that in the Deep South, at least three quarters of voters supported secession, meaning there were fewer than one in four who did not.
In the Upper South it was about two third secessionists, one third Unionists and in Southern Border States it was the reverse: about two-thirds Unionists, one-third secessionists.
So, all told, about 6% of the Union Army came from Confederate states, and another 8% from Southern Border States.
These were more than enough to compensate for deaths suffered by the Union Army.