But diplomats say Cameron has miscalculated the political game and could be slapped down, an outcome that would fuel the ugly debate in Britain about staying in the EU.
Cameron's argument is that Juncker, 59, is part of the pro-federalist old guard of politicians who were rejected by voters in last month's European Parliament elections. That ballot - characterised also by voter indifference and an economic slump in many countries - saw strong gains by far right and nationalist parties who say the EU project is a blight on sovereignty.
Cameron argues national leaders should have unfettered choice to name the president of the Commission, a body that wields great executive power, negotiates EU treaties with foreign nations and is in charge of the bloc's 142 billion ($222 billion) annual budget.
This right, though, has become a matter of debate. Under a treaty that took effect in 2010, leaders have to "take into account" the results of the European Parliament elections when appointing the new Commission chief. This fuzzy piece of text was cited by the Parliament to put forward a "lead candidate" - Juncker - who is backed by the pro-EU conservative bloc which gained most seats.
Juncker is straight out of the mould of moderate centre-right continental European politicians. Consensus-driven, he came to global recognition in the negotiations to fix the euro crisis.
Cameron has taken risks by pitching his flag on the field of national sovereignty, which Ukip has come to dominate in British politics. If the "lead candidate" process takes root, Cameron argues, national governments will lose their ability to block candidates they oppose, as Britain did in 1994 and 2004.
Meeting with other leaders ahead of the summit, Cameron appears to have believed he had rallied enough support, especially in northern Europe.
But his confidence seems to have been misplaced. The signals are that Juncker is acceptable or not worth fighting about, or that Cameron's stridency is irritating. For one thing, Cameron's Conservative Party walked out of the Parliament's centre-right bloc of MPs after he became party leader, arguing the group had become dangerously pro-integration. The irony is that Cameron's Euro-MPs forfeited the right to have a say in proposing the next Commission boss.
Cameron has threatened to put the issue to a vote if need be, a move that could prove to be divisive within the EU and worsen his humiliation if he loses.
Legally, leaders only need a weighted majority of votes, attributed according to a country's population, to approve the selection of the Commission president.
But the choice is traditionally done by consensus and no one has ever been selected before over the objections of one of the EU's biggest states. Cameron would need 38 per cent of the vote to muster a blocking minority.
Some analysts point to a possible behind-the-scenes deal whereby if Cameron backs away from forcing a vote, he will get some quid pro quo - a decision by the summit on the urgent need for EU reform, or perhaps the promise of a senior role for Britain's representative on the Commission.
Defeat in a vote or inadequate concessions would be crippling for Cameron, who has promised to stage an in-or-out referendum in 2017 if the Conservatives are returned to power in elections due next year.
