Sources tell CBS News it was Vice President Dick Cheney who delivered the pink slips; he and the president worried that the economic team didn't have the "gravitas" to instill confidence in Wall Street.
"They didn't send a message that we knew where we were going, we knew what we were doing and that was showing up remarkably in this economy that was going up and down," said Republican strategist Scott Reed.
CBS News Chief White House Correspondent John Roberts reports the treasury secretary had earned a reputation as a loose cannon on a tight White House ship, criticized for touring abroad with rock star Bono while the markets were tanking and frequently speaking at odds with the president.
Lindsey, while a close friend of the president, was considered an ineffective spokesman on economic policy.
Both had become liabilities as Mr. Bush prepares to roll out a new round of tax cuts to spark the economy, perhaps before Christmas. But Wall Street analyst Jim Grant cautions the markets need more than personnel changes to feel good again.
"Both are substantial individuals," says Grant. "It's not as if removing them is going to cure what ails us.
The housecleaning, which began Election Night with the resignation of SEC chairman Harvey Pitt, reflects profound concerns that the sputtering economy could be a drag on the president's re-election campaign. Mr. Bush remembers all too well what happened a decade ago to his father, another popular wartime leader whose re-election hopes were derailed by a stumbling economy.
"Everybody believes that these approval ratings are great, but they're also artificial," says Reed. "They could be popped very easily if the economy had some downturn."
Following plans laid weeks ago, Mr. Bush will quickly name successors and unveil a new tax-cut package, said advisers eager to portray the changes as a fresh start for the economy. New unemployment figures matched an eight-year high, underscoring the economic situation.
Prospects already making the rounds to replace O'Neill are Wall Street titan Charles Schwab, former House Ways and Means chairman Bill Archer, former Federal Reserve governor Wayne Angell and retiring Texas Sen. Phil Gramm.
Stephen Friedman, a member of the board of directors of Goldman Sachs, is the leading candidate to replace Lindsey. Another possibility is Glenn Hubbard, currently chair of the White House Council of Economic Advisers.
"I appreciate Paul O'Neill's and Larry Lindsey's important contributions," Mr. Bush said in a brief written statement. He did not address whether the pair resigned on their own, but administration sources told CBS News that O'Neill and Lindsey were asked to leave.
Senate Democratic Leader Tom Daschle called the firings "an overdue admission by the Bush administration that its economic policies have failed." But he said the shakeup was not enough.
"The fundamental problem is that this administration has no comprehensive plan to get the economy back on track," said Daschle, a frequent critic of the president's handling of the economy.
O'Neill, 67, was the first member of Mr. Bush's Cabinet to leave. White House officials said more high-profile departures could be coming, and already the rumor mill was buzzing.
Health and Human Services Secretary Tommy Thompson, often whispered to be headed back to Wisconsin, recently told his staff he was staying put. Environmental Protection Agency director Christie Whitman is said to be frustrated with her low-watt role inside the administration.
The White House has been at work for months on a new economic package centered on additional tax cuts for lower- and middle-income individuals, playing down the administration's earlier focus on business-side tax proposals to stimulate investment.
Other ideas on the table would be designed to encourage individual investors in the volatile stock market. Advisers are debating whether to time the plan's announcement around the president's State of the Union address in late January, or make it sooner to head off criticism.
O'Neill's two years at Treasury were peppered with controversy. He touched off a furor when he said he would keep nearly $100 million worth of stock in his former company, Alcoa, after being named to the Cabinet post. Under fire by critics about potential conflicts of interest, he eventually reversed course and sold the stock.
As the president's chief economic spokesman, he was frequently criticized as being either too enthusiastic about the economy's prospects and the stock market or too ho-hum.
"I think Paul O'Neill was the Jimmy Carter of treasury secretaries," said economist Richard Yamarone of Argus Research Corp. "He was a good and honest man with good intentions, but he just didn't get the job done. I don't think the administration's economic message got out. "
At first O'Neill's unscripted utterances were like a bit of fresh air, economists said. But on a number of occasions they rattled rather than soothed markets and even made white House aides nervous.
During a stock slide in May, O'Neill was in Africa with rock singer Bono, calling attention to the problems of the world's poorest continent, when he got irked at questions about his effectiveness.
If people didn't like his work, he said, he didn't care. "I could be sailing around on a yacht or driving around the country," he said.