I believe that success of a person mostly depends on chances. If he is lucky, he can be taught by good teachers, accompanied by good friends, and exposed to good experience or techniques. Money or education spending definitely, to the best of my belief, increases enormously the encounter rate of those opportunities.
Yes, educational spending does predict success to an extent. When children go to school in dilapidated and unhealthy buildings, it is difficult for them to learn. Wealthy districts also historically do better than districts located in poor neighborhoods because of the difference in tax bases between the two. The state should make up the difference so that poor neighborhoods can offer the types of educational programs that richer areas can offer.
The issue lies in where priorities lie. The amount of spending on education, statistically, is a key indicator that education is going to be higher, discipline is going to be instilled, and success is more likely. Those three items often go hand in hand. Also, many careers demand higher education degrees to get a foot in the door, so the more spending that happens, the more doors that will be opened.
In my opinion, spending does not always equal success in education or any other area. Our government is absolutely amazing at wasting money. So much of our tax dollars is going to programs that don't have a track record of success. This waste in education is one of the reasons I have chosen to send my kids to private schools.
Personally I believe that the federal government should pressure state governments to provide larger budgets for their education systems. Much more money could be spent on today's developing children, but I do not believe that any spending is necessary to indicate success. I believe that success is measured on it's own terms.