As Poland passed on the baton, the small Scandinavian country of 5.6 million -- one of the few in Europe with a left-leaning government -- will have to face head on the ballooning euro debt crisis.
But with the big euro nations of France and Germany seen as driving the crisis management, Denmark risks being marginalised along with the nine other EU members, including Britain, which have not adopted the single currency.
The importance and sway of the EU's rotating presidency has also dwindled since the Lisbon Treaty created the post of a permanent president of the European Council.
"Politically, Denmark will have little impact on the aspect of European cooperation that, for now, is mainly attracting attention," the Ritzau news agency said Sunday
"Formally, Denmark cannot and should not resolve the euro crisis," it added.
The news agency, however, hailed Prime Minister Helle Thorning-Schmidt and European Affairs Minister Nicolai Wammen for their expressed aim to try to bridge the differences between the 17-member eurozone and the full 27-member bloc.
"I understand perfectly that the 17 members of the eurozone need to take some decisions amongst themselves," Thorning-Schmidt said recently.
But it is in the interest of core EU members France and Germany "to keep the 27 together" and consult all EU member states "when these decisions concern them," because "in times of crisis, we have to believe in our institutions," she said.
Wammen meanwhile has stressed that Denmark's main mission during its six months in the EU driver's seat would be "to unify the countries that are in the eurozone with the ones that are outside of it."
That towering task has been further complicated by Britain's decision to leave the negotiating table at an EU summit on December 9, raising fears of a European collapse.
Wammen has said he wants to see London remain "a very active member of the European family," noting that Europe had to "find concrete solutions to concrete problems".
Swedish local daily Sydsvenska meanwhile predicted that Denmark would remain a "player in the power game" surrounding the euro crisis.
But as Denmark moves to the helm, Danes themselves are more sceptical than ever about the common currency, according to a Statistics Denmark poll published on December 21.
It showed that 71 percent of those surveyed were negative on joining the eurozone, to which Denmark had negotiated an opt-out following a referendum rejecting the Maastricht Treaty in 1992.
"The European debt crisis has affected Danish opinions on participation in the euro," Danske Bank analyst Steen Bocian said.
With little power to end the crisis, Denmark will likely instead "focus its political energy on having an efficient presidency in all the areas within the EU where Danish ministers are invited to sit at the negotiating table," Ritzau predicted.
Copenhagen has for instance said the Danish presidency would focus on renewable energies to bolster job creation and economic growth in Europe.
And if nothing else, the EU presidency offers Denmark a possibility to "make itself visible" in the cultural arena, Ritzau pointed out.
The small Scandinavian country has an ambitious cultural agenda during its six months at the helm, with events planned all over Europe promoting among other things Danish filmmaking and music.