Ms. Fiorina’s official title is chairwoman of the Republican National Committee’s “Victory ’08” committee dedicated to electing Mr. McCain as president, and she is typically described as an economic adviser to the candidate. To some extent, she is. But Mr. McCain’s campaign advisers say her real role within their testosterone-heavy circle matters more: A high-profile female face for a candidate whose support among women lags substantially behind that of his Democratic rivals.

“She has a great feeling for the economy, for technology and probably what women think about these things, and she’s wired in,” said Thomas J. Perkins, a pioneer venture capitalist and a leader on the Hewlett-Packard board in Ms. Fiorina’s ouster. (In the past, Mr. Perkins acknowledged, “we’ve had words and we’ve sort of attacked each other in print.”)

In turn, a number of Republicans say Ms. Fiorina is using the McCain campaign to rebuild her image after her explosive tenure at Hewlett-Packard. They also say it is hard to see why a woman widely criticized for mismanaging one of Silicon Valley’s legendary companies is advising and representing a candidate who acknowledged last year that he did not understand the economy as well as he should.

“Well, see, the good news about business is, results count,” Ms. Fiorina, 53, responded briskly in a recent interview in her office at Republican National Committee headquarters on Capitol Hill. “And the results have been very clear. The results have been crystal clear. From the day I was fired, every quarter, even before they had a new C.E.O., has been record after record. That doesn’t happen unless the foundation’s been built.”

Opinion is still split on whether Ms. Fiorina or her successor as chief executive, Mark V. Hurd, deserve credit for Hewlett’s success after Ms. Fiorina drove through the company’s $25 billion acquisition of Compaq in 2002. By many accounts, Ms. Fiorina was superb at marketing, mixed on strategy, bad at execution — and extraordinarily successful in unifying the board against what Jeffrey A. Sonnenfeld of the Yale School of Management calls her “street bully” leadership style.

Photo

“What a blind spot this is in the McCain campaign to have elevated her stature and centrality in this way,” said Mr. Sonnenfeld, the senior associate dean for executive programs at the management school and one of Ms. Fiorina’s sharpest critics. “You couldn’t pick a worse, non-imprisoned C.E.O. to be your standard-bearer.”

But Mr. McCain, as Ms. Fiorina put it, does “clearly not” share the views of her critics. To the contrary, he so proudly calls on Ms. Fiorina in her regular appearances with him on the campaign trail — he calls her an American success story “who began as a part-time secretary” — that he seems to be suggesting that Ms. Fiorina, true or not, might have a role in a McCain cabinet.

Advertisement Continue reading the main story

As a result, Ms. Fiorina has been buzzed about as a potential commerce or Treasury secretary or even as a McCain running mate, although some Republicans close to Mr. McCain swiftly dismiss the idea of her as vice president. But the view within the campaign is that it can only help Mr. McCain’s standing among women to have Ms. Fiorina mentioned as a possibility for high-profile office in a McCain administration, particularly when he is trying to win over the supporters of Senator Hillary Rodham Clinton.

Newsletter Sign Up Continue reading the main story Please verify you're not a robot by clicking the box. Invalid email address. Please re-enter. You must select a newsletter to subscribe to. Sign Up You will receive emails containing news content , updates and promotions from The New York Times. You may opt-out at any time. You agree to receive occasional updates and special offers for The New York Times's products and services. Thank you for subscribing. An error has occurred. Please try again later. View all New York Times newsletters.

In the meantime, Ms. Fiorina has done little to tamp down speculation that she might run for office herself, including the California governorship in 2010.

“I would be disingenuous if I said it has never occurred to me,” Ms. Fiorina said about running in general. “And in part it occurs to me because people keep asking. When I give speeches, people raise their hand — ‘run, run, run.’ ” For now, she said, “I’m focused on getting McCain elected.”

Ms. Fiorina has been a regular at the campaign’s Saturday policy sessions at headquarters in Arlington, Va. — she was part of a group, including the candidate, behind Mr. McCain’s sharp pivot from warning against government intervention in the mortgage crisis to calling for government aid to people in danger of losing their homes — but she does not serve as a bridge for the candidate to the business or financial community, in large part because of her tenure at Hewlett-Packard.

“It’s difficult to say that she is the unequivocal success figure that resonates with Wall Street,” said A.M. Sacconaghi, an analyst who tracks Hewlett-Packard for Sanford C. Bernstein & Company

Ms. Fiorina, whose late father, Joseph T. Sneed 3rd, was a conservative federal appeals court judge and a member of the panel that appointed Kenneth W. Starr as a special prosecutor into the Clintons’ Whitewater dealings, first met Mr. McCain after she testified on Capitol Hill in 2000. Mr. McCain had just abandoned his presidential run against George W. Bush and Ms. Fiorina, who asked to see the senator in his office, left impressed that he was savvy to technological innovation. “He just got it,” she said.

Ms. Fiorina, who is married to a former AT&T executive, Frank J. Fiorina, and has two stepdaughters, now divides her time between a condominium in Washington and a home in Silicon Valley. She received a severance package from Hewlett-Packard worth more than $42 million (Mr. McCain denounced excessive executive pay in an economic speech in Pittsburgh last month) and said in the interview that one of the biggest differences between her new life and her old is that “I’m not deciding.”

That was clear on a recent morning on the McCain campaign bus, when the candidate summoned Fortune’s onetime “most powerful woman in business” to sing to him and an audience of reporters in the back. The selection was “We’re Strong for Toledo,” which Mr. McCain had heard from Ms. Fiorina at an Ohio fund-raiser the night before.

Ms. Fiorina, embarrassed but not at all shy, did as she was told.

“Now we know the secret of her success,” Mr. McCain enthused when Ms. Fiorina was done with her serenade.