However, Deputy Prime Minister Nick Clegg, who heads the smaller, pro-Europe Liberal Democrats, denied that the coalition which took office under the Conservative Cameron in May 2010 might now collapse.
"It would be even more damaging for us as a country if the coalition government were now to fall apart. That would create economic disaster for the country at a time of great economic uncertainty," Clegg told a television interviewer.
Conservative Foreign Secretary William Hague echoed that view, saying it was vital for the coalition to continue as Britain teeters on the edge of another recession.
"Although some of these different views about Europe have come to the fore in recent days the Lib Dems are clear, as we are, that the coalition continues and that's in the vital interest of this country," Hague told Sky News television.
But the divisions run deep.
Clegg turned his fire on eurosceptic members of the Conservative Party who are pressing Cameron to follow up his veto on European Union treaty change with a referendum on ending Britain's membership of the 27-nation bloc.
"A Britain which leaves the EU will be considered to be irrelevant by Washington and would be considered a pygmy in the world when I want us to stand tall and lead in the world," Clegg told the BBC.
At a Brussels summit on Friday, Britain vetoed a plan for a new EU treaty that would impose closer EU control over national government budgets in order to curb the bloc's debt crisis. Cameron said the proposed deal risked exposing London's powerful financial services industry to unwelcome EU regulation.
The other member states, including the 17 using the euro, now plan to adopt a separate pact without Britain, leaving the island nation alone as never before in the EU, a club it joined in 1973 but which Britons have long viewed with distrust.
"I'm bitterly disappointed by the outcome of last week's summit, precisely because I think now there is a danger that the UK will be isolated and marginalised within the European Union," said Clegg, a former member of the European parliament.
"I don't think that's good for jobs, in the City or elsewhere, I don't think it's good for growth or for families up and down the country," he added.
Speaking of being informed of Cameron's veto in the early hours of Friday, Clegg said: "My immediate reaction was I said this was bad for Britain.
"I made it clear to ... the prime minister, of course, that it was untenable for me to welcome it. And now subsequently I said that I regret ... the outcome."
Other senior Liberal Democrats attacked Cameron and some took a swipe at the gloating eurosceptics on the right of his party.
Former Liberal Democrat leader Paddy Ashdown told Sky News the veto had been a "catastrophically bad move", accusing Cameron of "acting as the leader of the Conservative Party, not the Prime Minister of Britain."
On Saturday, Liberal Democrat deputy leader Simon Hughes said the coalition was "not a eurosceptic government" and that Cameron's restive right-wing should "calm down".
Clegg's tough talk, following initial loyal declarations of support for Cameron on Friday, may reassure supporters of his centre-left party, which formed an uneasy alliance with the Conservatives after an inconclusive election last year.
Support for the Lib Dems has halved to little more than 10 percent since the election, with many supporters unhappy with compromises they have made in government. Quitting the coalition now would leave the Lib Dems facing electoral disaster.
However, Clegg said he now wanted Britain to re-engage with Europe, putting him on a collision course with right-wing legislators in the Conservative camp. He said those cheering the outcome of the summit were "spectacularly misguided."
Nevertheless, a poll in the Mail on Sunday newspaper found a majority of voters backed Cameron over Europe. The research by Survation said 62 percent of the public were behind him, while only 19 percent said the prime minister was wrong to use the veto. The poll also found that 66 percent of those surveyed wanted a referendum over ties with the EU.
Cameron and Clegg are far apart on Europe. The prime minister styles himself a eurosceptic whereas the multilingual Clegg worked for the European Commission and cites his own family background - including a Dutch mother and Spanish wife - to explain his "internationalist outlook". His party has in part defined itself by its support for European integration.
"The Lib Dems are united on this from top to bottom. It could be a real problem for the coalition in the medium to long term," said Tim Bale, a politics professor at the University of Sussex.
