"God helps those that help themselves" is a phrase that is found in exactly ZERO verses of the Bible. It is often used as the rallying cry against welfare programs, social security, etc.
We are to help others while working to sustain ourselves and our faith.
"He who is not willing to work, does not eat."- 2 Thessalonians 3:10. Notice the word WILLING. The Bible does not say those who do not work. It says those who are not willing. Many are willing, but cannot (physical reasons, unemployment reasons, etc).
Of course, the main argument is one of semantics: "help themselves." How does one define such a thing? If I need to improve my financial situation and I am a hard worker who asks the boss for a raise, is that helping myself? In a way, of course. If a single person seeks companionship and they go out looking for someone, is that helping themselves find mate? Again, in a way, yes.
The Bible mentions that if draw closer to God, He will draw closer to us. This is often seen as a "meeting halfway" kind of thing, and often serves as the "biblical basis" for perpetuating the phrase and concept. The Bible also says "Faith without works is dead (faith)."
I believe we are not to sit around and be lazy about things. And, in a way, that is helping ourselves. But, I think the bigger picture is that we are not to help ourselves in the sense of a "name-and-claim-it" mentality nor a "snatch and grab" one. I also believe that the Lord helps plenty of people who CANNOT help themselves. Heck, the Bible is full of examples - healings, miracles, etc - where the people could not help themselves. Ah, but they were WILLING.
One of my favorite verses in the Bible comes from Isaiah: "But they that wait upon the Lord shall renew their strength; they shall mount up with wings as eagles; they shall run, and not be weary; and they shall walk, and not faint." They that wait... I have always seen this as a double meaning. On one hand, we are to wait, as in pray and listen and allow God to help us in our needs, our desires. On the other hand, we are to wait on the Lord, as in a waiter/waitress. That is, we are to work for God.
God's Grace is unwarranted, unmerited, undeserved. We get it not because we "help ourselves" and so He gives us some kind of reward. Rather, He gives it to us despite anything we try to do, and often in spite of the mess we often make of thing BECAUSE we try to help ourselves.
If we are only out to help ourselves for selfish reasons, the Lord is not going to help us.
The best way to find this out for yourself? Read the book.
As a side thought: one of my favorite (and most difficult) courses in college was Western Civ to 1650. In that class, the professor showed the historical ties between many events in the Bible and those documented in other forms. It was the first time I was shown the Bible as a historical text (as opposed to a purely spiritual one).
Another side note: The phrase is all-too-often misattributed to Ben Franklin's coinage. While he did USE the phrase, he did not COIN it. It's been around a lot longer than that. Look it up - that's a pretty good story, too.