At that time, the government quietly prints a bunch of USD and buys enough BTC with it to last a couple years. Money enters the economy. Huge inflation out of nowhere. US dollar loses confidence and inflation becomes hyperinflation. People run for BTC, and before long nobody wants to hold dollars any longer than necessary. All of a sudden, $15T+ doesn't sound that difficult to pay off, right? And the government changes the rules, makes BTC legal tender, and sends its creditors the pittance they're owed.
As long as Bitcoin is mainly traded against US dollars, it strenghtens the dollar. Reason is that most of the world population are not from the US.
Also - If a wealthy investor uses his Dollars to buy some guys bitcoins, that person is more likely to spend them on items and services than the investor was. This in turn strenghtens the dollar. It takes away idle/speculation money and puts them into the real market.