This phrase actually isn't found in the Bible, and while it is right up to a point, it isn't entirely accurate in light of the Bible's teaching. Let me explain.
On one hand, you are right: People need to work and be responsible for their actions, and when they aren't, society suffers (as do they). God didn't intend for us to spend our lives pursuing pleasure or ease; He gave us work to do, and even ordinary tasks are important when they are done for Him. The Bible says, "Whatever your hand finds to do, do it with all your might" (Ecclesiastes 9:10). When we do that, God will bless our labors.
But on the other hand, we are dependent on God for everything -- even the next breath we take. It's easy to forget this and think that we're strong enough to do everything we want to do -- but we aren't. We need to depend on God, and He should be at the heart of everything we do. The Bible says that He "is able to do immeasurably more than all we ask or imagine, according to his power that is at work within us" (Ephesians 3:20).
Never forget, however, that no matter how hard we work, we can never win God's favor or save ourselves by our own efforts. We need Christ, because even our best efforts are tainted by sin. Have you given your life to Him, and are you trusting Him alone for your salvation?