That is unlikely to be the result. The US national debt is over $21T now. $1T is <5%. Dumping that much on the market at once would certainly affect interest rates, but not at a catastrophe-inducing level, and all of the normal tools used to control interest rates remain available.
By comparison, the US deficit this year is ~$0.8T, i.e. the US itself is dumping nearly that amount into the market. The Quantitative Easing program after the housing crisis was $3.5T over a few years.
It's also unlikely that they would dump the entire amount at once, because causing a sudden short-term rise in interest rates is not to their advantage (they would take a bath on bond prices). But if they divested something like $100B/year, the effect on the market would be minimized.