Pay by check on Sunday online. I went and checked my history of payments and it seems Walmart is slow because every payment I have made has taken 3-5 days from when I initiated payment to it showing up on my bank. Leave Walmart out of it if you can. I think you will be okay.
Edited to add make sure you pay by 5pm ET on due date
I don't think I have ever had a scheduled payment come out of my account on a Sunday. When I used to pay things on Friday, it never cleared until Monday.
Walmart has always taken 48-72 hrs to clear a payment. if you pay on sunday it wont be processed til monday which starts the 48 hr clock. You should be fine. Even still your bank may take some time 24 hrs as well before the system denies the check.