I think with only a 30 minute turnaround time they are trying to see how hungry you are. After all who wouldn't want to hire a qualified person and pay less than they knew they had to pay?
I would examine why I wanted to leave where I was working and compare that to where you see yourself with the new company. Does the new company offer enough to make the pay cut worth it? Are there benefits involved to offset the pay cut? Maybe healthcare or a take home truck. What kind of review schedule does the new firm offer and how quickly can you make up the pay cut?
Make a counter offer of some sort that you are comfortable with and see how badly they need you.
