Yes, things could really nasty. In discussing the ways in which China might retaliate against tariffs, the Post told readers:
"China is also the largest foreign holder of U.S. government debt. It holds $1.17 trillion of U.S. Treasury securities, down about $33.5 billion since last August. The U.S. government faces huge borrowing needs, not only to finance new deficits but also to refinance past securities now coming due, so a drop in China’s appetite for that debt could nudge interest rates up in the United States."
The purchasing of US government bonds by China's central bank was the main tool through which it propped up the dollar against the yuan. The high-valued dollar makes Chinese goods cheaper relative to US goods, allowing it to run a large trade surplus with the United States.
If China were to sell some of the US bonds it holds, it would raise the value of the yuan, making US goods and services relatively more competitive. This is supposedly what both the Bush and Obama administrations wanted China to do. (I said "supposedly" because this was their public position. I don't know what happened in their private discussions.)
It is also worth noting that it appears Trump's major complaint is that he wants more protectionism in the form of stronger patent and copyright protections in China. If he succeeds in this effort, it will mean higher prices for consumers in both the United States and China. For some reason, the Post is not as concerned about the impact of these potential price increases as it is about the impact of higher steel and aluminum prices.