The debt ceiling is not enforceable considering the Constitutional powers granted to Congress (fourteenth amendment) and the mandate that it create (coin) the currency as needed for the common welfare (Article 1: Section 8). It, along with many falsehoods concerning finance/money creation that have persisted only because the voting polulace is econ illiterate have long ago reached their expiration date and are holding us back from realizing our potential as a modern economic force in the world.
Neither taxes nor bonds are "funding mechanisms" for the sovereign issuer of a fiat currency. Both require the existence of US dollars already created by Congress and serve primarily to regulate the "net" money supply, which is represented (to the penny) by the national debt. The private sector cannot be responsible for the repayment of that number without removing "ALL" existing currency from circulation, which would mean defaulting on all private bank debt as a consequence.
Both parties serve the same masters when they act out the drama of "debt ceiling" doom and gloom. They can only do so as long as we continue to spread their propaganda for them and not acknowledge the unique position of a "currency issuer", falsely equating it to our own experience with money as "currency users".
If either party were serious about reducing the (mostly) irrelevant number defining the debt they could simply stop selling Treasury bonds to match deficit spending. Then we would see their donors revolt and have a shot at regaining control of our government in the backlash.