Government debt equals private assets, and so being against government debt is being against (at least one form of) private assets.
If you are against the accumulation of private assets for whatever reason (for example, because you're a communist - see what I did there?), there are still better ways of preventing that than making the government commit economic suicide.
Honestly, the US should just get rid of the debt ceiling altogether, and recognize that the size of the budget deficit needs to be benchmarked not against pseudo-religious standards, but against how much productive capacity is available in the real economy - because that is what you need to look at to prevent inflation (which is the only possible negative economic outcome from a budget deficit that is too large).
Edit: I would appreciate some feedback on why people vote me down. I try to reply to questions and criticism as to the contents of what I write in a calm and clear fashion. I hope people don't just vote me down because they disagree with something that I write, or find it politically uncomfortable.