The Prime Minister looks set to force a vote in Brussels later this week in a bid to prevent the EU's top job going to a politician backing closer integration.
The Coalition Government is opposed to the frontrunner for the job, former Luxembourg prime minister Jean-Claude Juncker.
Yesterday in a sign of how high No 10 consider the stakes, it declined to rule out the possibility that Mr Juncker's plans could drive ministers to push for the UK to leave the EU.
Mr Cameron yesterday held "full and frank" discussions with the President of the European Council, Herman Van Rompuy, the man leading the search for his successor. But as they were meeting a recording of two Polish politicians suggested the scale of the uphill battle the Prime Minister faces.
Overheard was Poland's foreign minister Radoslaw Sikorski, a friend of senior Tories and a former member of the Oxford University Bullingdon Club at the same time as Boris Johnson.
In a translation of the tape, he is recorded as saying that Mr Cameron has "f*****" up his handling of the European issue.
He accuses the Tory leader of leaning on "stupid propaganda" in an attempt to appease Eurosceptics. He made his remarks while speaking to a former Polish finance minister Jacek Rostowski.
In comments that will do little to ease fears in Downing Street that Europe is heading in the wrong direction, Mr Rostowski said that no Polish government could agree to Mr Cameron's proposals for EU reforms "except in return for a mountain of gold".
A translation of the tape also records Mr Sikorski as saying that Mr Cameron has shown "not for the first time, a kind of incompetence in European affairs".
He accuses the Prime Minister of having "f***** up the fiscal pact" and adds: "He is not interested, he does not get it, he believes in the stupid propaganda, he stupidly tries to play the system."
But both politicians say that they are concerned about the potential for the UK to leave the EU.Mr Rostowski says such a move would be "generally bad for us, because we would like for Great Britain to stay". But he goes on to predict that Mr Cameron will lose his promised 2017 in/out referendum and that Britain would leave.
A second taped conversation shows the spokesman for Donald Tusk, the Polish prime minister, saying that Mr Tusk "f***** [Cameron] up good" during a row over plans to curt access to child benefit for Poles in the UK.
The recordings are part of a series that have been published over the last week.
European leaders are expected to discuss Mr Juncker when they meet in Brussels on Friday.
A No 10 spokesman said: "The Prime Minister asked President Van Rompuy to prepare the European Council for a vote on Mr Juncker's nomination, should the European Council choose to depart from a consensus-led approach when it meets this week. President Van Rompuy agreed to work through how a vote would proceed."
Asked if Mr Juncker's victory could eventually see UK ministers campaign for the UK to leave the EU a spokesman described the question as "hypothetical".