Prime Minister of Greece may be the worst job in Europe, but Lucas Papademos took it anyway. The bespectacled economist is expected to be sworn in on Friday, alongside a new Cabinet tasked with implementing a landmark bailout deal that everyone hopes will save the country — not to mention the entire euro zone.

As a former vice president of the European Central Bank (ECB), Papademos is well respected and already adept at negotiating with euro-zone heavyweights. He must act quickly to convince international lenders — a troika that includes the European Commission, the ECB and the International Monetary Fund — that Greece will stick to the bailout terms hammered out last month. While some details still need to be negotiated, the overall deal includes a major debt swap and is worth about $177 billion.(See photos of the protests in Greece.)

Greece’s partners need plenty of convincing after outgoing Premier George Papandreou’s unexpected announcement that he would ask his people to vote on the latest bailout terms in a national referendum — a move that left global markets reeling on fears Greek voters would scupper the plan. Indeed, the idea angered European lenders so much that they talked openly of forcing Greece out of the euro zone. France and Germany even froze the latest installment of their loans to Greece — some $11 billion — leaving its government without enough money to pay next month’s bills.

Most Greeks want to stay in the euro zone although they’re balking at the austerity measures Greece’s creditors have demanded. Papademos’ biggest challenge is trying to convince Parliament to approve further belt-tightening when people clearly don’t want it. Many worry more cutbacks will only exacerbate the social unrest that has plagued Greece since its first round of austerity measures 18 months ago, while others say the 64-year-old doesn’t have the savvy to handle both Greek politicians and antiausterity protesters, who have accused him of engineering a “financial coup” to assume leadership of the country.(See why there was no joy in Greece over the E.U. deal.)

“I am not a politician, but I have exercised economic policy in Greece and Europe,” Papademos told reporters outside the presidential palace in Athens on Thursday, just after he had been appointed Premier. He said his priority was to stay in the euro zone. “It won’t be an easy road,” he said. “But I’m convinced the problems will be solved. They will be solved faster, with less cost and more efficiently, if there is unity, agreement and prudence.”

Unity may be his biggest challenge in a country as polarized as Greece. Aside from fighting between its two main political parties — the center-left PASOK party and the center-right New Democracy party — left-wing parties have refused to join coalition talks and are demanding immediate elections. Meanwhile the leader of New Democracy, Antonis Samaras, effectively stalled negotiations by refusing to sign a document in support of the bailout agreement — part of the party’s bid to increase its advantage in next year’s elections by coming out against the new coalition government. As the fighting over who would succeed Papandreou dragged on, media reports varied wildly; first Papademos was in, then he wasn’t. Other names were floated. The leadership vacuum prompted one radio talk show to ask listeners to pick a Premier. They offered everyone from Vladimir Putin to Tintin.

See how Greece’s Prime Minister George Papandreou undid himself.

The political bickering has many Greeks exasperated. Sophia Palaki, who’s 31 and works in publishing, grew frustrated watching politicians argue at such a crucial time for the country. “I felt insecure watching them because I didn’t know what was going to happen,” she says. “I’m glad they finally chose someone because we must retain our place in Europe. Mr. Papademos seems responsible. I hope he can make things happen.”

On paper, Papademos looks like the right man for the job. He was educated at the Massachusetts Institute of Technology, earning a doctorate in economics. He took a job as chief economist at the Bank of Greece in 1985 and was appointed governor in 1994, staying in the post until 2002, when he moved to the ECB. He stayed at the ECB until 2010, when he joined the Kennedy School of Government at Harvard University as a visiting professor.(Read “Should Greece Ditch the Euro?”)

“He’s the man to execute a very specific plan right now,” says Theodore Pelagidis, an economics professor at the University of Piraeus. “Beyond that, it’s the hope that this coalition government will inspire new people to join Greece’s political class. This country needs more problem solvers.”

Vassilis Katsoulas, a 47-year-old security guard at the National Archaeological Museum of Athens, says he’s hoping the transitional government will help fix the inbred inefficiencies and corruption that are slowly strangling Greek society. Outgoing Premier Papandreou couldn’t do it, Katsoulas says, but he wonders who can. “Can a government of people who are good with numbers and following the rules get us out of this mess? I don’t know,” he says. “All I know is that my salary has been cut in half, and I am having a hard time keeping up with my bills.”

To succeed, Papademos and the new Cabinet must win the trust not only of European lenders but also of people like Katsoulas. While the Cabinet’s final makeup hasn’t been announced, Greek media have reported that Finance Minister Evangelos Venizelos will stay on the job, as will other PASOK ministers elected in 2009. There are also reports that Samaras’ New Democracy party will contribute four officials to the coalition while the right-wing LAOS party will have two ministry posts.(Read “The Hitch in Greece: The Nationalist Who Delayed the Transition.”)

“In Greece we have this ‘cult of the savior,'” says Yannis Palaiologos, editor of the newsweekly Free Sunday. “We expect someone to come and point with a magic wand and solve everything. That’s obviously not going to happen.”

It’s what many Greeks had expected of its outgoing Premier Papandreou, the 59-year-old scion of Greece’s most prominent political dynasty, before the debt crisis unhorsed him. Papandreou bid farewell to the nation in a televised address Wednesday, in which he wished the transitional government well. “It is obvious that in order to achieve this historic agreement, we would have to find a person who had everyone’s support,” he said.

At least until elections are held, which could happen as early as February, that savior is a technocrat with a quiet voice and a thorough knowledge of euro-zone economics. If Papademos is focused and effective, Palaiologos says, he could affect more than the latest bailout deal. Greeks may finally be able to ask themselves the question they have been avoiding during the past two years of economic and political instability: If austerity isn’t saving the economy, what will? It’s an answer that could make — or break — Greece and the euro.

See why Papandreou couldn’t hold onto power.