The situation you've described has never happened. Out of all the options, it is considered the safest. People forget that the dollar is backed by the ultimate currency - military force.
There is a possibility that members of Congress are actively seeking to undermine the financial strength of the United States, and to do so will not vote to raise the debt ceiling. Weakening the federal government is their goal, conservative social issues are merely justifications.
I’m not sure what relevance you think the military has here in this situation.
There are just a few members of Congress that meet that description, however. They only wield a lot of power when the rest of Congress is divided neatly into two nearly equal parts. The moment actual default becomes a real possibility, the mainstream members of both political parties will briefly form a consensus and kick that can down the road a ways. Just like they always have. Not too far, mind you, because it must remain something they can argue about periodically.
The bad part, of course, is they likely won't do that until we've already done some damage to our credibility.
If you're going to hold until maturity, I don't see how the debt ceiling affects you significantly (any more than it would affect the entire asset market). The treasury will pay you eventually, likely within days.
If you are holding 10 year treasuries and were planning on selling them on the secondary market in July, yeah that could be very bad.