The Constitution of the United States of America can make some interesting reading.
For example, Article I describes the Congress of the United States, how it shall be organized, how its members shall be chosen, and the powers it shall possess. Among its many powers, listed in Section 8, is “The Congress shall have power to make all laws which shall be necessary and proper for carrying into execution the foregoing powers, and all other powers vested by this constitution in the government of the United States, or in any department or officer thereof.”
If upholding the good name and credit of the United States is a necessary and proper activity, which many believe it is, then I would say that Congress does not have the power to fail to make a law necessary for the government to borrow money, and enable it to carry out its obligations to pay its bills, or repay its debts.
If my understanding is correct, the president need not bargain with the Congress to raise the debt limit; it is obliged to do so, and if Congress elects to add irrelevant portions to its bill, he may veto it, and continue to veto any further obligatory bill containing irrelevancies, until Congress produces a “clean bill,” authorizing the president to protect the financial responsibility of the United States, and fulfilling its obligations to its citizens.
Eliminating contention over the means to unilaterally force each other to act, Congress and the president can concentrate on finding and implementing mutually held goals.