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evand comments on Open Thread, December 16-31, 2012 - Less Wrong
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Given the amount of debris, and recent trends in launch costs, launch rates, space project completion times and budgets... I'd say decades sounds entirely reasonable. If we had a more serious launch infrastructure in place, it might be done in a few years. Right now, we might get a useful pilot result in a few years if we started a high-priority project today. It would be more years before the project was operating at a useful rate, and yet more to finish cleanup.
Part of the problem is that very small objects moving at high velocity are problematic, and there simply is no easy way to catch them without creating more such objects. At present, many serious proposals actually involve handling every piece of debris individually. That's expensive, to say the least. Other proposals involve complicated stuff with deploying large objects like thin films, threads, etc., which is an activity with a very poor success rate thus far.
My point is that taking those trends as a given after a Kessler syndrome catastrophe - when substantially all technology that relies on LEO satellites no longer work - is a strange presumption. Current trends contain very little information about what would happen if LEO were unusable.
If GPS stopped working, the US government would fund its replacement solely to regain the military advantage it provides. Likewise, telecommunications companies would be irrational if they refused to devote a substantial portion of their potential revenue to re-building the capacity that earns them billions in revenue.
In short, the lack of resources currently devoted to clean-up may not be maximizing expected value - but there's substantial resources that would become available if failure to provide them would leave LEO unusable for multiple decades. Taxes would be raised, private bonds would be floated, environmental regulations would be waived or amended, but LEO would be made usable.
The problem is not the funding, it's the lack of anyone to give it to. The Apollo program had von Braun. We don't have a replacement for him. Musk is close, but unproven. The answer is not any of the other existing companies, or today's NASA, or JPL. That's not an organization you can just create with money.
No one today knows now to build what we need in that time frame.