Practically speaking, Treasury collects enough revenue in a month to pay interest, Social Security and active military, which combined represent about a quarter of what's owed.

But bills come due every day and the revenue available to Treasury differs, sometimes radically, from day to day.

For instance, the Bipartisan Policy Center estimates that $30 billion of interest will be due on Feb. 15, but only $9 billion in revenue would be available to pay the $52 billion in legal obligations due that day.

What's more, Treasury's systems -- which process more than 80 million payments a month -- are set up to pay bills as they come due without regard to the type of payment. Interest payments, however, are processed separately.

By most accounts the payment system is a complicated one. So it's not clear how long it would take to make changes to allow Treasury to prioritize.

And there's concern that any temporary band-aid to a debt ceiling impasse would not do much to protect the U.S. economy let alone its reputation with creditors.

The Center estimates that, absent an increase in the debt ceiling, Treasury would only be able to pay about 60% of what's owed, meaning reams of delayed payments. That could take a big bite out of economic growth. And being late on so many payments would likely "prompt a downgrade even as debt obligations continued to be met," credit rating agency Fitch said this week.

- CNNMoney's Mark Thompson contributed to this report.