Well I'm on my 5th day now.
It bothers me when customer service is unable (or unwilling?) to provide me with a reason for the delay. If dreamhost says "Payments are cashed out on the 1st business day" then I expect payment on the first business day, or at least an explanation when it doesn't happen, I don't think that's unreasonable.
I'm a bit surprised and disappointed by this and I hope it's a one-time thing. (I also hope customer services slow response time doesn't continue in future)