My direct deposit never hit until Thursday night/Friday morning. I remember reading here that Target Credit Union account holders got access early. I don't know if other credit unions also do.
Also, my store only held actual checks for a few days and mailed whatever hadn't been picked up. If the paper copy was just a pay stub, those didn't get mailed ever. There were a few times I'd have 4 or 5 sitting there waiting for me. Since I had direct deposit, I simply didn't think about collecting the stub. And my day job doesn't issue paper stubs at all.