You literally told her how long it would take you. That should have been the end of the discussion. Not simply disregarding your estimate because it wasn't what they wanted to hear.
If someone asks me when I can have something done, I give them a realistic and reasonable estimate with a bit of padding. Most of the time they dont really care, they just want to know when they can expect it.
It has been a challenge for our team to get other people to understand what our bandwidth is. They would just keep asking and asking. So we started giving estimates to everything and showed them how much we could fit into a given week and how long it would take to get through all their requests. We got 2 new head counts soon after.