NEW YORK (CNN/Money) - President Bush's new economic team will have a big job ahead of it -- breathe life into the comatose U.S. economy, win Wall Street's confidence and keep Bush's 2004 re-election campaign from looking like his father's 1992 bid.

On Friday, Treasury Secretary Paul O'Neill and senior White House economic adviser Lawrence Lindsey resigned -- at the suggestion of the White House -- about a month after Securities and Exchange Commission Chairman Harvey Pitt submitted his resignation.

Friday's head-rolling came just after the Labor Department said unemployment jumped to an eight-year high and businesses slashed tens of thousands of jobs from non-farm payrolls in November.

The report, much worse than most economists expected, highlighted the maddeningly slow nature of the economy's recovery from a recession that began in March 2001 -- and probably gave Bush hair-raising visions of the "jobless recovery" that ran his father out of office in 1992.

Since O'Neill and Lindsey were seen as taking a relatively laid-back approach to the economy, at odds with the more nervous views of Wall Street, their departure could mean Bush and Co. will take a much more aggressive approach to the economy.

"The administration is likely to push for more fiscal stimulus, and this makes it a little more clear-cut, because O'Neill had been hesitant about that," said Joshua Feinman, chief economist at Deutsche Bank Asset Management.

That stimulus could take several forms -- Bush and other Republicans have been talking for months about making last year's tax cut permanent, and other tax reform and spending measures could follow.

"My guess is there will be a bigger stimulus package in the months ahead -- more than $50 billion -- in response to frustration they can't get the economy moving faster," James Glassman, senior U.S. economist at J.P. Morgan, told CNNfn's Market Call program.

Though some economists are uncertain that some of Bush's proposals -- the permanent tax cut, for example -- will necessarily help the short-term economy as much as it hurts the country's long-term budget situation, most agree that businesses are going to need some incentive to hire more workers.

With inflation dead in the water and companies unable to raise prices in order to support profits, businesses have been squeezing more work out of fewer workers as a way to keep costs low. Without a pickup in demand for their goods, businesses will have little reason to increase production so much that they'll need more workers.

"You need to help the cash flow to businesses, just to make them a little better off," said Joel Naroff, president and chief economist of Naroff Economic Advisors.

The new economic team also might need to be a little better at simply holding the confidence of business leaders; O'Neill's relentless cheerleading of the economy at times when a more hard-nosed approach might have been more appropriate raised fears on Wall Street that O'Neill and other Bush advisers were out of touch.

"There's a danger in being too positive, of there being a huge disconnect between how positive a policy-maker sounds and what the economy is doing," said Anthony Chan, chief economist at Banc One Investment Advisors. "That was probably one of O'Neill's greatest shortfalls -- the dichotomy became too wide."

Wall Street's lack of confidence in Bush's economic team was dramatically illustrated by the action of stock prices Friday morning. After the Labor Department reported the big jump in unemployment, stocks looked set for another day of brisk selling. But when the news of the O'Neill and Lindsey resignations crossed the wires, stocks turned positive and stayed that way the rest of the day.

"They could have done more to communicate well with Wall Street," said Brown Brothers Harriman economist Lara Rhame. "The new [people] will be much more savvy, more public-relations oriented."

Speaking of public relations, it seems unlikely that it was a mere coincidence that the resignations -- which had been rumored for months -- happened to be announced immediately after devastating economic news.

"The interesting thing is that they did this on a day when economic information came out that was decidedly weaker than expected. It blunted what could have been a pretty bloody response," said John Davidson, president and CEO of PartnerRE Asset Management. "The resignations might have been planned for some time, but the fact that they were a secret and were released on exactly this date and at this time turned out to be very effective."

Of course, if he's going to keep Wall Street -- and voters -- happy for more than one day, Bush will need more than crafty public relations tricks.

"Bush needs pretty quickly to turn this economy around," Davidson said. "If we languish for the next two years, it'll be the last two years of Bush's presidency."