Why is there a US idiom of using China to mean far away?

Solution 1:

Dig to China

As Americans have a general notion that China is on the other side of the world, the hyperbole dig to China, emerging in the late 19th c., seems an inevitability:

When the shaft, which is 14x6½ feet, had reached a depth of one hundred and eleven feet below the surface, Mr. R.'s foreman and other experienced miners were of the opinion that further search would be fruitless; but Mr. Redhead was confident, and, to use his own expression, was 'bound to dig to China, or find coal.' Des Moines Leader, 4 June 1873. Cited: History of Polk Co., Iowa, 1880.

The citizens here use cistern water, but about one mile from the town is never failing water, which shows that we wouldn't have to go all the way to China to get that precious necessity by means of wells, and lots of it at that. Belton (TX) Journal, 12 Jan. 1882.

“This is my ground, every inch of it—sixty feet wide, one hundred feet long, four thousand miles thick. Yes, sir, every inch, if I choose to dig to China. …” — Edith Keeley Stokely, “Mr. Potter's Neighbors,” The Ladies’ World 17.6, June 1896.

Source: Harper’s Bazar 35.5 (Sept. 1901), 482.

Four months later, the text appears sans cartoon in a humor column in an Australian paper, where it makes even less geographic sense.

Children: We're goin' to dig to China.
Minister: What for ? -
Children: 'Cause you said on Sunday they were living in darkness, and we're going to let in some light. — Northern Star (Lismore NSW), 4 Jan. 1902.

Slow Boat to China

As an idiom, slow boat to China was apparently well-known among those who gambled at cards prior to the 1948 Frank Loesser song of that name, but appeared in print (Washington Post, 23 Dec. 1947, p. C8) only months before the song was copyrighted. The idea is that a steady loser of large amounts of cash would be the perfect gaming companion on a slow boat to China. To hear the song, you have your choice of Ella Fitzgerald, Bette Midler and Barry Manilow, or this somewhat frightening Swedish woman channelling Billie Holiday. The song propelled the idiom into the broader language, even to the halls of government:

The poor Hudson—the slow boat to China—was receiving her beating. — Jack Kerouac, On the Road, 1957.

So they figured out at the White House the thing to do to get fast action was to get a bill through the Congress. Now if there is any slower slow-boat-to-China way of getting tariff relief for a specific product, than by trying to pass a bill through the Congress, I do not know what it could be. — Charles H. “Charlie” Brown (D-MO), Congressional Record, House, 22 Aug. 1957.

I want to see newspapers from Halifax to Victoria by air—and not by slow boat to China, because that is not good enough. I can remember how hard it was to get news about Canada when we were in New Zealand. — Canada, House of Commons Debate, 3 Feb. 1966.

Here, of course, it’s the time of the voyage in the foreground, not merely the distance.

Timbuktu

For many Europeans, the ancient city of Timbuktu in West Africa has been the very definition of an exotic “middle of nowhere” ever since the hyperbolic images of wealth and culture in the 1550 Della Descrittione dell’Africa of Leo Africanus. As one blogger explains:

When my grandfather wanted to signify something far out of reach or unimaginably far away, the thing or person would be “way out in Timbuktu” or “gone to Timbuktu.” As a child I loved the word’s percussive sound and exotic aura. … It was years before I learned that Timbuktu existed outside his imagination. I also learned that for centuries of Western history, the imagination had been Timbuktu’s main location. — Steve Kemper, “In the Labyrinth,” 3 May 2012.

Yet for Alexander von Humboldt, China was at least one station on journeys to the far corners of the world:

Was die Landreisen anbetrift, so sind dieselben in neuster Zeit nicht so ausgedehnt, als im Mittelalter: damals war es keine Seltenheit, dass ein Europäer die äusserste Gränze von China erreichte, dann nach Timbuktu gelangte, und endlich in Corduba ankam …

As for overland journeys, the most recent ones are not as extensive as they were in the Middle Ages: at that time it wasn’t a rare thing for a European to reach the furthest border of China, then Timbuktu, finally to arrive in Córdoba… — Alexander von Humboldt, Lectures on Physical Geography, University of Berlin, transcribed, Gustav Parthey, 1827/8.

In choosing a metaphor, the cultural distance is more important than the physical one. The longest non-stop flight today, for instance, is Singapore Airline’s Dallas/Ft. Worth–Sydney route of 16–17 hrs., but Australia is simply not exotic enough for the metaphor.