Congress permitted President George W. Bush to accumulate new powers in the executive,
and these powers have passed to Obama. Bush succeeded in establishing that, as a wartime commander-in-chief, he had the "inherent power" to disobey the laws against torture, spying on Americans without obtaining warrants, and indefinite detention. In addition, Bush used signing statements in ways inconsistent with his oath and obligation to uphold the laws of the United States, and he took the U.S. to war based on lies, deception, and fabricated "evidence," an offense that qualifies as treason.
With these precedents, it is a simple matter for President Obama to declare that, with the U.S. at war in a world of growing instability, he has the inherent power to ignore the debt limit and to continue financing the government with the creation of new money by the Federal Reserve.
Congress could try to protect its loss of the power of the purse by impeaching Obama. But how credible would it be to impeach a wartime president who is using the same "inherent power" of his office that Congress permitted the previous president to use?
As President Bush's acts were not deemed impeachable offenses, it seems likely that Congress has lost its power to impeach through default.