The debt-ceiling is what makes that whole exercise constitutional to begin with. Congress said: "okay, Treasury can borrow money, but only up to this much." If the executive disregards the debt ceiling, that would break the fiction of delegation, and the executive will have fully wrested a fundamental Congressional power away from Congress. That's the same reason why the 14th amendment cannot override the debt ceiling. Yes, the debt ceiling is a statute. But without it, Treasury has no power to issue any debt.
Hope the Republicans enjoy the civil rights violation lawsuits from everyone who suffers actual damages when their mortgage interest rates go up due to the Republican's violating the 14th Amendment so that the Republicans can benefit from that fallout. Especially now that the head of the Republican party is on the record stating that a failure to raise the debt limit will benefit the Republican's politically come election time.