European Commission President Jean-Claude Juncker at a recent news conference. (Olivier Hoslet/European Pressphoto Agency)

For Jean-Claude Juncker, the new president of the European Commission, the honeymoon is over and some in Europe already want a divorce.

The prime minister of Luxembourg for the better part of 18 years, Juncker took over the European Union’s top job Nov. 1 only to be hit by calls to resign a few days later. The sniping came after a group of investigative journalists issued a report detailing secret deals struck by major corporations with Luxembourg that allegedly allowed them to shave billions of dollars off their global tax bills.

On Wednesday, Juncker personally responded to the allegations for the first time, taking political responsibility “for what happened in each and every corner and quarter” of Luxembourg during his tenure. But he said the deals in question had been struck with independent tax authorities, while also insisting that they complied “with national legislation and international rules.”

But he conceded that some of his country’s tax rules might not have been in line with “ethical and moral standards that are generally applicable.” Nevertheless, he said he would push for streamlined tax codes across Europe and vowed that he could be relied on to fight tax evasion. He said he would not step down.

The E.U. Competition Office is investigating Luxembourg — as well as Ireland and the Netherlands — for sweetheart tax deals. But thus far, there have been no official charges­ of wrongdoing.

A host of critics, however, are calling the fresh revelations evidence that Juncker is the wrong man for the job. Some are going even further, saying the scandal is exposing a woeful lack of democracy at the top of E.U. power structures.

The European Commission president wields sweeping authority over the creation of laws and the legislative agenda for the 28-nation bloc. But it is a job that is still not filled by voters and that, especially this year, was decided on via a backroom political deal.

Before assuming his new role, Juncker had been forced to step down as prime minister in December amid charges of corruption and over­reaching within Luxembourg’s spy agency. He denied any wrongdoing and sought to segue his career by slipping into the job of European Commission president.

Previously, Europe’s elected heads of government had largely nominated candidates. But despite strong reservations from some E.U. leaders, including British Prime Minister David Cameron, Juncker managed to secure the job through a new “spitzenkandidaten” (or lead-candidate) system that came into effect this year.

Political groups in the European Parliament, including members of German Chancellor Angela Merkel’s Christian Democratic Union, agreed to support certain candidates depending on the results of its May elections. As it turned out, the bloc backing Juncker emerged the strongest. But a study by one group, Open Europe, showed that the center-right parties backing Juncker were supported by only 9.7 percent of the European electorate.

The scandal now, said Raoul Ruparel, head of economic research at Open Europe in London, is another example of “the view that there is a huge democratic deficit at the center of the E.U.”

He added, “No one really was making the connection between tax issues and Juncker’s candidacy beforehand, and I think that also highlights the lack of scrutiny going on at the very highest levels of the E.U.”

For the E.U., the scandal could not have come at a worse time. Juncker is being expected to restore confidence in Brussels, the E.U. administrative capital. But particularly after the European debt crisis, that is no easy job. Today, its image as a hub for knotted bureaucracy, inefficiency and Machiavellian deals is as strong as ever.

A pull-no-punches Bloomberg View editorial this week declared: “Jean-Claude Juncker needs to go.” It accused him of presiding over Luxembourg as it used “Swiss-style bank secrecy” and “government-blessed tax avoidance schemes” to become a haven for 340 major corporations and investment funds eager to avoid taxes.

How did the little Grand Duchy do it? By granting some firms a corporate tax rate below 1 percent for profits funneled through Luxembourg, providing an avenue for companies — allegedly including the likes of Pepsi, Ikea and Coach — to exploit loopholes in the countries where the majority of their profits were being made.

In Britain, Stewart Jackson, a Conservative member of Parliament, told the Daily Mail that Juncker’s position was now “untenable.” Margaret Hodge, a Labor MP and chairwoman of Britain’s public accounts committee, told the Guardian that “it is outrageous that [Juncker] is now representing the E.U. at the G-20 on tax evasion.”

But many nations — including Germany — are openly supporting Juncker, and most observers think he will survive this early storm.

“I believe he will stay,” said Olaf Boehnke, head of the Berlin office of the European Council on Foreign Relations. “There are too many influential people in Europe who want to keep him where he is. And so far, none of this seems to have been illegal. It really comes down to a question of reputation.”

Karla Adam in London and Stephanie Kirchner in Berlin contributed to this report.