There was a time when Treasury Secretary Timothy F. Geithner seemed to be the most unlikely person President Obama would send to negotiate with Congress.

Democrats and Republicans faulted him for his role in the bank bailouts during the worst of the financial crisis — some critics blaming him for paying too much attention to the needs of Wall Street and not enough to ordinary Americans, others for the lethargic state of the economy.

Geithner himself has said he might not be the right guy to oversee negotiations over tax and spending policies, telling the New Republic last year that “you want somebody in this job who can bridge the political world in a different way than I can.”

But there Geithner was Thursday on Capitol Hill, heading into critical meetings with the Republican and Democratic congressional leaders, Obama’s choice to be the senior negotiator on behalf of the White House in discussions about averting the “fiscal cliff.”

Geithner plans to step down in January, and the fact that Obama has selected him to lead the negotiations shows how much the president has come to rely on his much-maligned Treasury secretary. Geithner has overcome early struggles and frequent criticism to become someone both Republicans and Democrats want to work with.

“I think he’s thoughtful. He’s deliberate. He’s well-respected by all parties. And he’s someone who understands all the different pieces of this very complex puzzle,” said Rep. Chris Van Hollen (D-Md.), who met with Geithner on Thursday. “He’s got sort of a panoramic view of the political landscape.”

Republicans, who earlier said they appreciated Geithner’s role in fiscal policy discussions over the past year, said Thursday they were frustrated with the path he took. In meetings, Geithner reprised White House proposals to significantly raise taxes on the wealthy while launching a round of economic stimulus.

People close to Geithner and to the White House say he was chosen to lead the discussions because he can make clear for Republicans what Obama will and won’t accept, while at the same time be frank with Democrats about the need to make concessions on entitlements, such as Medicare.

Geithner has been able to rehabilitate his reputation with both parties over the past two years. According to some Republicans, he’s market-savvy, willing to make a deal and supportive of aggressive action to slow government borrowing. Democrats, meanwhile, say they have come to appreciate how strongly he defends the social safety net — for instance, Medicare and Medicaid — and how willing he is to spar publicly with Republicans.

Through a spokeswoman, Geithner declined to comment.

To a degree, the choice of Geithner to oversee the “cliff” talks is more stylistic than substantive. The details of a deal are being negotiated on a daily basis by White House and congressional staff members, and Geithner was accompanied in his meetings Thursday by Rob Nabors, Obama’s chief legislative liaison. Other key members of the team include White House chief of staff Jack Lew, National Economic Council director Gene Sperling and Sperling’s deputy, Jason Furman.

Some Republicans say they are pleased that Obama tapped Geithner for the role over Lew, who was a key negotiator during much of last year’s discussion over raising the government debt limit. Republicans claim Lew would not make compromises needed to close a deal. They say Geithner, by contrast, was willing to push both the White House and the Republicans, adding urgency to the talks by warning of the dire consequences for the country if they failed.

“Geithner was an asset to me in this whole thing,” House Speaker John A. Boehner (R-Ohio) told The Washington Post’s Bob Woodward in an interview for his book “The Price of Politics.” “God bless him, but he was the guy running around yelling, ‘Fire!’ And every day with the president, he’s screaming, ‘Fire!’ And you know if it weren’t for Geithner, I don’t know if the president would have gotten engaged like he did.”

Lew’s defenders note that he has been working on bipartisan deals for decades, as budget director in the Clinton administration and as a senior congressional aide before that. During his time at the Obama White House, they say he has always followed the negotiating strategy set by the president. And they say his role has not been diminished.

Inside the White House, Geithner has been at the forefront of pressing for ambitious deficit-reduction plans that would trim federal borrowing by about $4 trillion over 10 years. He has pushed for higher taxes on the wealthy at politically inopportune moments — such as in the middle of the 2010 congressional election campaign, when Democrats were sensitive to talk of tax hikes — and also pushed for changes to entitlements, prompting resistance from liberal White House officials.

Four years ago, when he met with Obama right after his election as president, Geithner argued against his own appointment. Having played a central role in the unpopular financial bailout, Geithner worried he would not be seen as an agent of change.

The weak economic recovery led to escalating calls among Republicans for his resignation, while Democrats took aim at the housing policies he helped oversee. Geithner, by his own admission, has never been a terribly effective communicator, and he did not embrace the public relations aspects of the job.

By the time of the debt-limit debate in the summer of 2011, Geithner had accomplished his primary job as Treasury secretary — stabilizing the financial system and restoring the U.S. economy to growth. With Washington turning to the debate over taxes and spending, a battle that could turn as much on political acumen as economic analysis, Geithner decided he wanted to step down, joining his family, who had returned to New York for his son’s final year of high school.

Amid financial turbulence in Europe last year that threatened the U.S. economy, Obama personally lobbied for Geithner to stay — even pressing Geithner’s wife, Carole — and successfully persuaded him.

The announcement that Geithner would remain at the Treasury came on the same weekend that Standard & Poor’s downgraded the U.S. credit rating — something that Geithner had predicted would never happen. S&P cited U.S. political dysfunction, saying that it was skeptical that policymakers would follow through on an agreement to slow borrowing.

“They drew exactly the wrong conclusion,” Geithner told CNBC after the downgrade. “Faced with tremendous challenge, our country has shown a unique and extraordinary capacity over time to act really with a tremendous record of judgment.”