No for several reasons with one overarching theme: a federal government debt is not a per se bad thing and is typically a good thing. I will explain.
First, the US continuously repays its debts; it only borrows new money after the fact. Plus, debt repayment is still less than 6.6% of the federal budget and less than 1.4% of GDP. If I spent only 6.6% of my income on a mortgage, I would save several months of mortgage payments each year. If I only spent 1.4% of my income on a mortgage, I'd be able to afford a multimillion dollar mansion. Therefore, the debt isn't nearly as big an issue as typically claimed.
However, suppose it was. Then what? In that case, the federal government cannot get in over its head because the congress defines what counts as a "dollar" and repaying debts is easy when One gets to decide what and how much is used for repayment.
Suppose, however, those debts must be paid in dollars as We know them today. The deficit and accumulated debt would still not be an issue because much of the debt is owed to various federal agencies. In other words, the federal government has borrowed the money from itself.
What if those debts were repaid? Would there be an issue with the remaining debt? No. As Alexander Hamilton noted in the earliest days of the republic, a government debt, if not excessive, gives creditors a vested interest in the economic health and well-being of the nation. Which means other countries buying US debt is an inherently good thing for Us because those countries then want to protect Us and help Us grow and thrive. Without that foreign debt, countries would have less incentive to be helpful and peaceful with Us and likely lead to increased wars and lower incomes all around.
But what about that word "excessive"? What happens when it gets excessive? Fortunately, We have never gotten to that point and probably never can because, as a debt starts to become excessive, interest rates would jump up and act as a metaphorical "brake" on borrowing, preventing that excess.
So, since the deficit and debt are not real issues and at best the policy equivalent of invisible intangible Dragons breathing room temperature fire, the idea of "raise the debt limit only if We balance the budget" is a solution in search of a problem and would actually cause problems instead.