NEW YORK (CNN/Money) - While there was a growing consensus that Securities and Exchange Commission Chairman Harvey Pitt had to go, finding a replacement everyone can agree on will be a tough job.

Pitt's Tuesday night resignation under pressure set off immediate speculation on who his replacement will be.

Democrats, the main critics of Pitt and the administration's handling of corporate corruption issues, lost control of the Senate Tuesday along with much of their leverage to block a replacement candidate. Still, the administration will want to be careful in naming a successor. Administration officials told reporters Tuesday there won't be an immediate replacement, adding that Senate confirmation of a nominee is expected to be difficult in the intense political climate.

The highest-profile name mentioned for the job is former New York Mayor Rudolph Giuliani, Time magazine's Man of the Year last year, who was a major campaigner for Republican congressional candidates in this year's election.

When asked if he would consider the SEC chairmanship if asked by President Bush, Giuliani told CNN's Larry King, "I don't have an interest in another job right now." Giuliani has been a business consultant since leaving office in January. Before he became mayor in 1994, he came to public prominence as the U.S. Attorney who pursued cases against some high-profile Wall Street figures.

CNN has learned that other candidates under consideration include Frank Zarb, who retired a year ago as chairman of the National Association of Securities Dealers; Assistant U.S. Attorney General Michael Chertoff, the head of the Justice Department's criminal division; outgoing Oklahoma Gov. Frank Keating, who previously served as an FBI agent, a U.S. Attorney and Assistant Secretary of the Treasury; Joseph Grundfest, a former SEC Commissioner who is now a Stanford University professor of law and business and an expert in securities regulation; and former top SEC lawyer James Doty. Doty had no comment when contacted by CNNfn.

AP reported that former SEC Chairman Richard Breeden was said to have been informally approached about the job but declined. But a spokeswoman for Breeden said he has not been contacted. Breeden now is a court-appointed monitor for WorldCom, one of the companies that has been plunged into bankruptcy by questionable accounting practices.

Pitt has offered to stay on during a transition period, an SEC spokeswoman told Reuters. But Bush could opt to name one of two other Republican SEC commissioners as an interim chairman. The two, Paul Atkins and Cynthia Glassman, declined to comment on the matter.

Other possible permanent successors to Pitt could include corporate lawyer Gary Lynch and former federal judge Stanley Sporkin, people familiar with the matter told Reuters.

CNN's Tim O'Brien takes a closer look at Harvey Pitt's resignation and possible successors. Play video (QuickTime, Real or Windows Media)

Sen. Richard Shelby, the Alabama Republican poised to become chairman of the Senate Banking Committee and whose criticism over the weekend eroded Pitt's previously solid Republican support, said Tuesday: "The process of what happened and how it happened was very troubling, and I think it tainted the whole situation."

To replace Pitt, the White House must find someone who is "able, experienced and above reproach," Shelby told Associated Press.

John Galvin, president of research firm SEC Insight, told CNNmoney Morning Wednesday that Pitt failed to demonstrate that he was an advocate for shareholders and was seen as closer to Wall Street brokerage houses and U.S. companies than to either big institutional investors or individual investors. But Galvin said he thought a middle of the road candidate is needed now.

"We don't think it's in the investing public's interest to have someone extreme on either side," he said. "You don't need somebody to pound the table and go after scalps in public corporations and accounting firms, but you don't need someone who coddles up to them either."

A dramatic drop in confidence in the way corporations report results has been widely cited for the stock market's sharp declines this year, but it is far from clear whether investors will embrace Pitt's departure, or his eventual successor.

For the markets, "the real issue is the election," said Arnie Owen, managing director of equities at Roth Capital Partners in New York. "The Pitt issue has been going on for a couple weeks. I don't think it will matter for the markets."  

from staff and wire reports