Randomly spotted snippet from this article:
Outside the White House, more and more prominent Democrats are questioning whether the debt limit is even constitutional.
Let's have a look, shall we?
Article. I. Section. 8. The Congress shall have Power... To borrow Money on the credit of the United States;...
So, yes: if Congress has delegated that power to the executive, then the delegation is unconstitutional. Only Congress has the authority to borrow money on the credit of the United States.
Likewise, I've held for many years that the War Powers Resolution is unconstitutional in that it delegates to the executive the power to start a war. (Responding to a war started by someone else is another matter entirely, but deciding to start a war absent an attack or imminent threat thereof is clearly a power of Congress, and may not be delegated.)