Hatch said the administration was refusing to "even have a conversation" over reducing the soaring cost of the government's big benefit programs such as Social Security and Medicare, the federal health care program for the elderly.
"If the Obama administration won't negotiate on entitlements in the context of the debt limit, when will they negotiate on entitlements," Hatch asked.
Lew said that the government's payment systems were not designed to allow him to pick and choose which bills. He said the government's computer systems issue around 80 million payments each month.
"Prioritization is just default by another name," Lew said.
Lew said default would cause serious damage as outlined in a report Treasury issued last week.
That report, Lew said, "points to the potentially catastrophic impacts of default, including credit market disruptions, a significant loss in the value of the dollar, markedly elevated U.S. interest rates, negative spillover effects to the global economy and real risk of a financial crisis and recession that oculd echoe the events of 2008 or worse."
In 2008, a serious financial crisis pushed the U.S. into the deepest recession since the 1930s.
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Associated Press writer Stephen Ohlemacher contributed to this report.