If your agent is not embarrassed to present the offer.... you are offering too much for the house.
Bottom line it really depends on where the house is and at what price range. A lot of factors go into way a house is still sitting on the market (ie bad marketing, cracked slab, pricing, title issues, ect.)
If it is a short that has been on the market for a long time, that is pretty normal.
If it is a REO you might want to bring your contractor with you.
Bargain hunting is not easy and it takes time and effort - you can not expect to submit 5 offers and get the deal you are looking for, it may be at 55 or 105 offers you will find the deal you are looking for.
Using cash or if you are pre quailed - they are about the same,
the banks want to know that you will be able to deliver and close the deal.
Where the difference comes in on cash is if it is a true cash offer with no contingency's
I have seen low ball cash offers with no contingency's beat out a pre approved loan offer.
The less red tape a seller/bank see's on your offer the more appealing it will be to them
If you find a home that you really like it is no time for low ball offers you need to sit down with your agent and really go over the comps and put your best foot forward.
Write the offer you are most comfortable with. If you do not get it then you know it was not meant to be.
If you do get it you know you got a good deal because you did your home work and you did what it takes to get the home.