You are apparently assuming that the “status quo” would be otherwise preserved. Well, it ain’t gonna be status quo at all. In fact, it’s gonna be utter chaos nationwide (& worldwide). When survival is the name of the game, world financial markets pale in comparison.
Real wealth is found in the ingenuity of free-thinking people, not in governments. The “national debt” is made out of play-money anyway, so-to-speak.
Are we talking about some sort of chaotic collapse of the US or a peaceful negotiation between a seceding Texas and the US? If the former, then all bets are off. But if we're talking peaceful secession, then assets of the US government, such as military hardware, would have to be returned to the US- seizing such equipment would most likely be an act of war. Similarly, any peaceful resolution would involve Texans taking their share of the debt, if they ever wanted to be treated seriously by other countries (or ever again trade with the US). Texas has received the benefits, such as they are, of Federal spending, just like anyone elese, and Texan politicians are just as responsible for the debt as the rest of Congress. You don't get to just walk away from an obligation like that and screw the remaining 49 states.