President Bush will "cast a wide net" in the search for successors to Treasury Secretary Paul O'Neill and senior White House economic adviser Larry Lindsey, who resigned Friday.

White House Press Secretary Ari Fleischer said Friday that the president has a history of promoting from within the government as well as looking outside the bureaucracy for good help.

O'Neill and Lindsey handed in their resignations on Friday after taking considerable criticism from Washington and Wall Street about their lackluster performance in rebounding the economy.

Fleischer neither confirmed nor denied that O'Neill and Lindsey were forced out, although other White House sources said the men were told their departures would be welcome.

When asked last month, Bush gave no indication that the two were on their way out.

"My economic team came in during very difficult times. There was a recession; there was a terrorist attack; there were corporate scandals. We have done a lot to return confidence and to provide stimulus through tax cuts. My economic team developed a tax cut package, sold the tax cut package, is implementing the tax cut package. And for that, they deserve a lot of credit.

"We're making good progress on the economy. There's still work to do. And I appreciate the hard work of the economic team," he said.

With the two expected to be gone by the end of the month, several names have quickly risen to the top of the heap of possible replacements, including several who are widely respected by Wall Street.

Wall Street is already weighing in on the replacements, and its voice is being taken more seriously since the lukewarm market is seen as a reaction to Wall Street's arms' length relationship with O'Neill, former Alcoa chairman, and Lindsey, a past governor of the Federal Reserve, who were accused of being indifferent to market concerns.

If Wall Street's approval is indeed important for economic policy, some of the frontrunners to replace O'Neill may include discount broker Charles Schwab as well as New York Stock Exchange head Charles Grasso; former UBS PaineWebber chairman Don Marin, who was in contention for the job before O'Neill was chosen; and Joseph J. Grano Jr., head of UBS PaineWebber in New York.

Former General Electric CEO Jack Welch — despite his well-publicized marital problems — would also be the type of character to whom Wall Street would respond.

Retiring Sen. Phill Gramm, R-Texas, has had his name thrown into the mix as well. But Gramm has just taken a lucrative post and is said to be eager to make money after 30 years in public service. Another possibility is businessman Steve Forbes; however, famous past run-ins between Forbes and both Bush presidents make his nomination less likely.

Lindsey's position could be filled by Glenn Hubbard, head of the White House Council of Economic Advisers and former Federal Reserve Governor Wayne Angell, an earlier candidate for the top treasury post, has been holding private meetings with Vice President Dick Cheney in recent months.

Securities and Exchange Commission Chairman Harvey Pitt has also resigned his post and a replacement has yet to be designated. One name frequently mentioned is former Clinton Chief of Staff Erskine Bowles, who lost the North Carolina Senate race last month but is widely regarded for his business acumen.

More shoes could drop before the clean-up is completed.

Fox News' Neil Cavuto and The Associated Press contributed to this report.