I posted recently about this problem and got some great advice. For another newish quilter here are some other things to consider:
I had not ironed my backing - when I did I gained more room than I thought possible. Not inches and inches, but ... a little bit.
I am bringing the backing over for the binding and do not have to have more than ... an inch? smaller? At least not as much as I sometimes have.
If all else fails and I really don't want to use your great suggestions I can trim a tiny bit off both top and bottom - 1/2 inch from each gains an inch overall.
It's not even pinned yet, but it's all laid out and ... I think I can make it work.
Here's the post where I showed the top.
http://www.quiltingboard.com/t-129716-1.htm