Fourteenth Amendment to the United States Constitution
The validity of the public debt of the United States, authorized by law, including debts incurred for payment of pensions and bounties for services in suppressing insurrection or rebellion, shall not be questioned.
When the Congress passes spending bills it not only authorizes the spending but the borrowing of money to accomplish the necessary spending if necessary. For the President not to spend the money as Congress has demanded by law is to fail to uphold his oath of office.
If Congress then passes a law limiting spending with a Debt limit, it has passed a law that will not meet the muster of Constitutionality. If Congress does not raise the limit or pass a new law that removes the original requirement to spend, the President is required by Law to create enough funding to meet the law. The Debt limit becomes null & void.