Lew said Obama has not changed his opposition to coupling a bill to re-open the government and raise the borrowing authority with Republican demands for changes in the 3-year-old health care law and spending cuts.
Boehner insisted that Obama must negotiate if the president wants to end the shutdown and avert a default that could trigger a financial crisis and recession that would echo the events of 2008 or worse. The 2008 financial crisis pushed the country into the worst recession since the Great Depression of the 1930s.
"We're not going to pass a clean debt limit increase," the Ohio Republican said in a television interview. "I told the president, there's no way we're going to pass one. The votes are not in the House to pass a clean debt limit, and the president is risking default by not having a conversation with us."
Boehner also said he lacks the votes "to pass a clean CR," or continuing resolution, a reference to the temporary spending bill without conditions that would keep the government operating. Democrats argue that their 200 members in the House plus close to two dozen pragmatic Republicans would back a so-called clean bill if Boehner just allowed a vote, but he remains hamstrung by his tea party-strong GOP caucus.
"Let me issue him a friendly challenge. Put it on the floor Monday or Tuesday. I would bet there are the votes to pass it," said Sen. Chuck Schumer, D-N.Y.
In a series of Sunday television appearances, Lew warned that on Oct. 17, when he exhausts the bookkeeping maneuvers he has been using to keep borrowing, the threat of default would be imminent.
"I'm telling you that on the 17th, we run out of the ability to borrow, and Congress is playing with fire," Lew said.
Lew said that while Treasury expects to have $30 billion of cash on hand on Oct. 17, that money will be quickly exhausted in paying incoming bills given that the government's payments can run up to $60 billion on a single day.
Treasury issued a report on Thursday detailing in stark terms what could happen if the government actually defaulted on its obligations to service the national debt.
"A default would be unprecedented and has the potential to be catastrophic," the Treasury report said. "Credit markets could freeze, the value of the dollar could plummet, U.S. interest rates could skyrocket, the negative spillovers could reverberate around the world."
Private economists generally agree that a default on the U.S. debt would be extremely harmful, especially if the impasse was not resolved quickly.
"If they don't pay on the debt, that would cost us for generations to come," said Mark Zandi, chief economist at Moody's Analytics. He said a debt default would be a "cataclysmic" event that would roil financial markets in the United States and around the world.
Zandi said that holders of U.S. Treasury bonds would demand higher interest rates which would cost the country hundreds of billions of dollars in higher interest payments in coming years on the national debt.
Sen. Ted Cruz, R-Texas, a force in pushing Republicans to link changes to the health care law in exchange for keeping the government running, spelled out his conditions for raising the borrowing authority.
"We should look for three things. No. 1, we should look for some significant structural plan to reduce government spending. No. 2, we should avoid new taxes. And No. 3, we should look for ways to mitigate the harms from 'Obamacare,'" Cruz said, describing the debt ceiling issue as one of the "best leverage the Congress has to rein in the executive."