The case for a strengthened Libertarian and Green Parties?

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Neither of those parties have the potential to become a real mass party capable of challenging either the Democrats or the Republicans. Any potential mass third party would have to have a stable group of supporters that compose a non-negligible portion of the population (which rules out the upper middle class Libertarians and Greens entirely), as well as a stable base for funding and party outreach and development.

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I think that a third party could operate within the existing order of things, provided that it was able to capture a fairly stable amount of electoral votes every cycle. A hypothetical labor party would probably do fairly well in the rust belt, for example. Provided that it could win the rust belt every cycle, and perhaps expand their base to throw the election to the House, and we could end up talking about electoral reform that ends the electoral college. Trust me, a third party strong enough to send an election to the House two or three cycles in a row is going to make electoral reform a very big priority, especially if the House that elects the President isn't the majority party among the electorate.