By Stephen Gandel
July 24, 2013

FORTUNE — Eliot Spitzer might have a higher bar to clear than he thinks.

When the former New York attorney general and governor announced he was running for New York City comptroller in early July, arguing that the job holds untapped potential, the unsaid flip side of that statement was this: Spitzer thinks the guy currently in the job, John Liu, is doing a lousy job.

Sipping on a smoothie at the Whole Foods in Columbus Circle, Manhattan, Liu takes Spitzer’s criticism in stride. “We have responsibility and we exercised that responsibility to steer the direction of the companies we own,” he says.

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In an article in Slate, published in late 2011, entitled “We own Wall Street,” Spitzer wrote that public pension funds, managed by state and city comptrollers around the country, should push for changes on Wall Street and within Corporate America in general.

Liu says he’s done just that in his oversight of New York City’s pension funds, which have a combined $140 billion in assets. On Spitzer entering what had been a one-man race for NYC Comptroller, Liu — who is running for New York City mayor — says, “My first reaction was that it was great there was going to be a primary. My second reaction was, ‘Couldn’t it be anyone other than someone who has broken the law.’ ”

A recent report from proxy advisory firm ISS credits Liu’s office with successfully leading campaigns to curb executive pay, and says it “scored a victory” striking deals with Wall Street firms to improve their clawback provisions to recover bonuses from negligent traders and bankers. A similar report from Glass-Lewis last year cited the New York City pension funds for its vocal push for Wal-Mart (WMT) to improve its regulatory controls in the wake of allegations that the giant retailer bribed officials in Mexico. Wal-Mart eventually added two independent directors to its board, which was unusual for the company, which has mostly had an insider board.

Liu says his office lead the charge against troubled energy company Chesapeake (CHK), helping to oust its CEO, who was allegedly striking side deals that would benefit the hedge fund he was running in his spare time, and completely rework the company’s board of directors. And Liu claims he pushed big banks to adopt new controls over their foreclosure practices.

Outside of corporate governance, Liu was early in calling for an audit of CityTime, New York City’s payroll system, calling Mayor Michael Bloomberg to task for problems with the program. Federal prosecutors have since concluded that hundreds of millions of dollars were misspent on the project.

Recently, he criticized Bloomberg for offering tax breaks to big companies. Liu voted against a tax deal for New York City-based grocery delivery service Fresh Direct. “Do you really think they are going to move jobs out of the city,” says Liu. “We need to take back tax breaks that we give to big business, and give them to small businesses.”

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Spitzer was forced to resign as governor of New York in 2008 after evidence emerged that he that he had hired prostitutes and tried to cover up pricey wire transfers. Spitzer declined to offer comment for this story. A spokesperson for his campaign says Spitzer was “not criticizing John Liu or any other person who has held the office, but thinks the New York City comptroller is a voice of the institutional investor. He looks forward to expanding that role.”

On Tuesday, Spitzer’s campaign released its first ad for the New York City comptroller race in which he apologizes for his past behavior. “Everyone, no matter who you are, deserves a fair shot,” Spitzer says in the ad. “I’m asking voters to give the same for me.”

Liu’s success in the comptroller’s office hasn’t provided much of a boost to his run for New York City mayor. In a recent New York Times poll, he ranked fifth in the race, with just 7% of those surveyed supporting his candidacy. Liu’s campaign has been dogged by allegations of illegal fundraising. In May, the former treasurer of Liu’s mayoral campaign and a donor were found guilty of creating straw donors on Liu’s behalf in order to game the city’s campaign finance rules. Liu claims that he is the most investigated candidate in history, and that he has been found guilty of nothing. Liu also says that he does not accept campaign donations from Wall Street firms.

Liu has seven full- time staffers devoted to corporate governance issues, out of a total staff of 758 in the comptroller’s office. That’s down from nine under his predecessor William Thompson, who is also running for mayor. Liu and his staff have filed about 60 shareholder proposals a year in the three years Liu has been in office. That’s down from Thompson as well. But Liu appears to have had a much better success rate in getting his proposals passed than his processor did. Still, pushing for such things as increased disclosure and accountability within Corporate America is an uphill battle. Like his predecessor, and other pension fund leaders around the country, most of the shareholder proposals Liu puts up get voted down. For instance, Liu publicly pushed and voted for a proposal at JPMorgan Chase (jpm) to strip CEO and Chairman Jamie Dimon of one of his titles in the wake of its $6 billion trading loss. The effort failed.

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Still, “elevating” the office to push for more change in Corporate America, as Spitzer has said he wants to do, will be mighty tough, even for someone like Spitzer. While New York City is a large investor through its pension fund, most of the money is invested in index funds. Companies are not as likely to listen to so-called passive investors because such investors are less likely to sell than those who invest directly in the company.

Spitzer could decide to take a more active role in running NYC’s pension fund and investing directly in companies he would like to change. But that could open the fund up to losses, something that probably won’t play well with union representatives who are the fund’s trustees. “Easy to say you are going to be more active, but it’s a balance and where you strike that balance is a challenge,” says Bob McCormick of Glass Lewis, which advises institutional shareholders on corporate governance issues.

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