Don't be dramatic. The US debt limit is $31.4 trillion, and the current level of the
US national debt is $31.7 trillion. The debt ceiling was reached on January 19, 2023, in other words, the technical default has already occurred.
This is what I think is true, but do not know for a fact.
Yes, we have exceeded the debt limit. But, and a very big but, the people in the treasury, and/or other agencies, are prioritizing the items to be paid right now and no due bills have been missed. That says that technically speaking, we have not defaulted. However, they can only juggle a few weeks more before there are actual defaults.