I am of the opinion that an agreement is the best course but that the President can act by himself and ignore the debt ceiling but that is opinion. There are arguments on both sides.

Article 2 Section 3 of the Constitution says of the President:
… “he shall take Care that the Laws be faithfully executed” …

So if congress passes a budget that requires borrowing by spending more than revenues, the President has a duty to borrow so he may execute the laws. It would seem unfair and perhaps unconstitutional to limit his abilities.

The President has an obligation to execute the laws. It is impossible to execute all laws since the debt ceiling law denies him the money to execute many laws, and so he has no choice but to ignore the debt ceiling law unless Congress increases the debt ceiling. By failing to increase the debt ceiling in a timely manner, Congress is blocking his constitutional obligation.

So it seems to me there are 2 good arguments in favor of this. First, the President is in a situation where he cannot execute all the laws so he must pick either this one debt ceiling law or all the others. The second is that the debt limit law is unconstitutional since it prevents the President from carrying out duties specified in the Constitution.

On the other hand, Article 1 Section 8 of the same Constitution gives Congress the power “to pay the Debts” and “To borrow Money on the credit of the United States” so maybe there is a Constitutional case for the debt ceiling. But then nowhere does it say that Congress can refuse to pay debts or limit the ability of the President to carry out the laws that they passed.

And nowhere does it say that the President cannot borrow in order to carry out the laws.