"If congressional Republicans refuse to pay America's bills on time, Social Security checks, and veterans benefits will be delayed. We might not be able to pay our troops, or honor our contracts with small business owners. Food inspectors, air traffic controllers, specialist who track down loose nuclear materials wouldn't get their paychecks," Obama said.
When he did mention debt, it was not in the context of the government delaying payments. Instead he spoke of questions that might be raised by financial markets.
"Investors around the world will ask if the United States of America is in fact a safe bet. Markets could go haywire, interest rates would spike for anybody who borrows money," Obama said.
The change from payments that "will be delayed" to market reactions is significant.
There is no clear legal authority for the president to prioritize payments, deciding which bills to pay and which to delay. Some say it would be illegal for the president to refuse to pay for spending authorized by Congress. Others believe there is a mandate to pay debt before other obligations. Some legal scholars argue that Obama's is only faced with illegal and unconstitutional options—and so should choose the least unconstitutional options. One recent paper said that president should just ignore the debt ceiling and issue debt.
Ultimately, none of these questions have ever been tested.
Obama's remarks today indicate that he does not consider ignoring the debt ceiling an option. Likewise, he rejected any of the various contrivances (such as using a platinum coin or the 14th Amendment) offered by various people outside the administration for escaping the limitations of the debt ceiling.
With default off the table now too, it looks as if prioritization is the administration's plan in case the debt ceiling impasse continues. This would likely mean the shut down of many important government functions. But it also means we will avoid the worst case scenario of the U.S. government defaulting on its sovereign bonds.