In testimony before the Senate Finance Committee, Lew said that trying to make such perilous choices between paying veterans or Social Security checks is not a good option and risks the first default on U.S. debt in history. He repeated the administration's demand that Congress pass legislation needed to end a partial government shutdown and raise the country's $16.7 trillion borrowing limit.
President Barack Obama was to meet later Thursday with top House Republicans at the White House to seek a path beyond a confrontation that has left the government shuttered for close to two weeks.
"The president remains willing to negotiate over the future direction of fiscal policy, but he will not negotiate over whether the United States should pay its bills," Lew told the committee.
Lew's testimony came after a day of activity but no real signs of progress.
Obama on Wednesday had House Democrats over to the White House. And Republican conservatives heard a pitch from the House Budget Committee chairman, Rep. Paul Ryan, R-Wis., on his plan to extend the U.S. borrowing cap for four to six weeks while jump-starting talks on a broader budget deal.
The deal Ryan proposed could replace cuts to defense and domestic agency budgets with cuts to benefit programs like Medicare and reforms to the loophole-cluttered tax code. Curbs to "Obamacare" were not mentioned.
At the hearing, Sen. Orrin Hatch, R-Utah, accused the Obama Administration of intentionally scaring the public and financial markets over the borrowing limit, "in an apparent effort to whip up uncertainty in the markets."
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.
"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 country into the deepest recession since the 1930s.
Associated Press writer Stephen Ohlemacher contributed to this report.