Apparently not, because when I told the tech I would need it that day and why, his response was:
"Well, you should have planned ahead better. Then, you wouldn't be having this problem."
I hung up on him because I didn't know what else to do. I called the my doctor and explained what happened and thankfully, they called back 5 minutes later and said it was ready to pick up. My husband went to pick it up and said the guy I spoke to on the phone was manning the register, but he was nice and said he's glad we got it sorted. I'm guessing he realized what he said, or the doctor set him straight.
Edit: the pharmacy is the HEB in Leander, TX. I realized I forgot to include that in my original post. They also tried to bill me without insurance and said the insurance company refused to pay because it was "too early," but I called the insurance company before calling them to refill it and they said it was no problem, so my husband had to call them again while at the pharmacy to prove it. They did end up fixing that quickly though.