You need to know three things:
1) What the market rent is
2) What amenities the average unit has at that average rent
3) What is your tolerance for an empty unit
If your rent is average and they just want a discount stay the course you may get a call back once they've shopped around. If your rent is a hundred dollars higher than average, in most markets, that is with in what is tolerable if you have a reason for it. Is the average unit 3 beds one bath and you have a 3/2? Does the average unit have street parking and you have a driveway and garage? That worth a hundred dollars easy to the right person.
However, if you just have an average unit, haven't had much interest and you rent is a hundred dollars more than the market then you will need to drop the price to be competitive. Even if you feel your unit is nicer do the math. I once calculated that it was better for me to rent a unit at a discount if it enabled me to rent in immediately than wait. This was during winter months when there isn't a whole lot of interest to move. I found when I listed it at the higher price that I still had enough interest I decided to hold off and wait for the right tenant but by the time I found a qualified tenant, a month had gone by, and that's money I'll never see again.