if the US government does default, that will probably cause the prices of Treasury bonds to go up , since a government debt default is a crisis and crises cause a flight to safety and the safest assets are, still, Treasuries:

This is certainly not our modal view, but in the unlikely event of a technical default, we think Treasury yields would decline and the curve would steepen. This seems unusual in the context of a default, but Treasuries have rallied into the latter stages of other serious debt ceiling debates in 2011 and 2013.

Money Stuff: Can Markets Handle the Debt Ceiling? by Matt Levine ✉️