What the 10% does is help one to keep their focus on the Lord in many areas in their life.
When one is consistant soon the blessing will over flow and it has happen for many of the LDS that have been faithful.
Some still are caught because of debt and living beyond one means and it dose make it a struggle to fullfil. Yet when the effort is applied along with prayer and daily scripture reading the Lord is able to free up those forces that was holding one hostatge. There are endless stories of where folks were in great trouble money wise and when they learn the laws of money they are amazed how the same amount could meet those obligations. And the door opens for an increase in funds.
This is learning how to exercise faith and grow in the ways of the Lord! One of the ways to exercise the Spiritual muscle!
I will not post a LONG treatise on this issue here, as others have chosen to do, but I will refer you to Biblical teaching on this subject. The Christian and Government: Paying Your Taxes
The relevant section is about 1/3rd of the way down, under the heading:
2. In Israel. When God established the nation of Israel, did He have a taxation system?
a) The Lord's tithe
I humbly offer this lesson as a means of expanding the discussion and bringing another perspective to the issue. Please take the time to read it, it is very well done.