I found support for Schiff's claim in the classic work, Commerce Defended, by James Mill. And I quote:
...a nation always has within itself a market equal to all the commodities of which it can possibly have to dispose; that its power of purchasing is always equivalent to its power of producing, or at least to its actual produce; and that as it never can be greater, so it never can be less. Foreign commerce, therefore, is in all cases a matter of expediency rather than of necessity. The intention of it is not to furnish a vent for the produce of the industry of the country, because that industry always furnishes a vent for itself.
Mill here is writing this as a corollary to to the famous Say's Law, which states that when you make something, that which you made can be traded for something you want. In other words production of Thing A gives you the ability to buy what you want of Things B, C, D etc.
That being the case, if a Chinese manufacturer makes a washing machine, he can trade it for a new Chinese car. So all the Chinese have to do is trade with each other, and they will find a market for all their products.
And now we give the floor to our good friend Devil's Advocate, who will ask a few question about Say's Law and this corollary:
DA: Dave, what Say says may apply to the rich capitalist owners of the factories, but what about the coolies who get paid 14 cents an hour? They don't get a new washing machine to trade for a car. Only the owners get washing machines to trade with, and how many cars do they need? You'll have ten thousand washing machines, ten thousand new cars, and only two men who can afford anything. The washing machine company owner can buy one new car, the car manufacturer can buy one new washing machine, and that's all they need. The coolies are stuck with nothing, and the owners are stuck with 9,999 cars and washing machines they will have no choice but to sell to the US.
SD: Not quite, DA. What if the washing machine company was owned by twenty partners?
DA: OK, then there would be twenty cars sold.
SD: And if it had thousands of partners?
DA: But it doesn't.
SD: Oh, yes it does. Because all the workers in the factories all over China are in reality partners in the companies they work for.
DA: What are you talking about? They are the exploited proletariat, not partners.
SD: Actually they are in a much better position than partners. A partner gets his share only when the product is sold, obviously. The workers get paid in advance. A partner gets paid nothing if there are no sales. The workers gets paid win or lose. A partner has to put up some money to be accepted as a partner. The workers get a slice of the pie even though they put up no money. So that it's not just the factory owner putting the washing machines on the market to trade for cars. It's him and all his workers.