Settling the Solar System will be essential for the long term survival of the human race. Nobody who understands the science involved seriously disputes that. Earth will only be able to support an advanced human civilization for a limited time, especially one with several billion individuals. That time may be thousands more years, or hundreds, or fewer.
The question really is how to expand out, and when. Humanity has the scientific knowledge and technological base to begin the expansion now. There is no guarantee either or both will be maintained indefinitely. A few private companies are currently working to find ways to make profits in space, and their ranks could easily grow. The governments of several major nations are considering plans to establish a manned lunar base fairly soon-- a key next step out. The time to make the fundamental decision would seem to be now.
Working out the how is another matter, but the basic building blocks could be those private companies, augmented by many major corporations representing a range of industries, and those governments already looking outward. Forging a public-private consortium that included corporations and governments would extend legal authority and legal protection of investment, property, and patents beyond Earth, creating whole new industries and vastly expanding the human economy. National governments would benefit by encouraging scientific breakthroughs and technological advances, by being part owners of those new industries, by building huge tax bases in the New Prosperity, and by maintaining some control over the pace and direction of change.
If humanity is to begin settling space yet this century, something like the partnership scheme sketched above may be the most viable approach.