Together, the commercial banks’ heavy reliance on the central bank to finance their everyday business needs, along with the growing borrowing burden for Spain and Italy, raise the risk of failure for some banks within the countries that use the euro and the danger that nations much larger than Greece could eventually seek a bailout or be forced to leave the euro currency union.

European stocks were down broadly on Tuesday’s gloomy news. In the United States, stocks closed lower, too, but were not down as much as they had been before the International Monetary Fund announced at midday that it would extend a six-month lending lifeline to nations that might seek it in response to the euro zone crisis.

At the same time, though, the central bank continued to resist calls that it stretch its mandate and expand the money supply, as the United States Federal Reserve and the Bank of England have done.

The European debt crisis has crimped the flow of funds to banks by raising doubts about the solvency of institutions with a large exposure to European government debt. In particular, American money market funds have severely cut back their lending to European banks in recent months, leading many institutions to turn to Europe’s central bank.

Compounding the problem, many banks using the euro have also had trouble selling bonds to raise money that they can lend to customers. That raises the specter of a credit squeeze that could amplify an impending economic slowdown. In addition, some banks may fail if they are unable to raise short-term cash.