David Cameron was facing growing questions on Tuesday evening over whether his plans for a powerful new press regulator, backed by legislation, would work.
Financial Times editor Lionel Barber became the latest senior figure to voice concern over the proposals agreed at late night talks between the three main political parties and the Hacked Off group, which has led the campaign for tighter press regulation.
Mr Barber described the discussions - at which the press were not represented - as a "horse traders' ball" and said his newspaper had yet to decide whether it would sign up to the new arrangements.
"This has not been a satisfactory process. We have not decided at the Financial Times whether we are going to join up with the new regulator. We will be looking at the practical implications and, above all, what has been completely lost in this process, the cost," he told BBC Radio 4's The World At One.
"I am worried about the practical costs of, for example, allowing free access to arbitration, I am worried about claims-farming, vexatious complaints from readers and others who will tie us up in knots. This is a real problem."
The FT had been among the papers most sympathetic towards the idea of a regulator established by royal charter - which the plan envisages - and Mr Barber's comments represent a setback for the prime minister, raising questions as to how many newspapers will join the new system.
Alan Rusbridger, the editor-in-chief of Guardian News and Media, was broadly supportive of the new arrangements, although he too expressed "grave reservations" over measures to enable the courts to impose exemplary damages on papers which do not sign up.
"The regulatory settlement is by and large a fair one, with compromises on all sides. We retain grave reservations about the proposed legislation on exemplary damages," he said.
"The agreed terms are not ideal, but after two years of inquiry and debate we finally have the prospect of a robust regulator that is independent of both press and politicians. It's a big improvement on what went before."
Other national newspapers have been more critical, with the Daily Mail Group, the Telegraph Media Group, News International and Northern and Shell issuing a joint statement saying there were "deeply contentious issues" still to be resolved.
The Daily Mirror denounced the plans in its editorial, while The Spectator magazine made its view clear in a front page that simply said "No".
The Newspaper Society, representing the UK's 1,100 local newspapers, has also condemned the scheme outright, warning that it would impose a "crippling" burden on local media.
Only The Independent has indicated it is ready to sign up, arguing in its editorial that it was time to "accept the new system and move on".
One of the Hacked Off representatives at the talks, Hugh Tomlinson QC, said the press had no right to carry on lobbying ministers over the issue, insisting they must now accept the findings of the Leveson report.
"We don't think they are entitled to lobby," he told the Commons Culture, Media and Sport Committee.
"There was a public inquiry where they were represented by a total of eight or 10 different QCs who argued their case, they have brought their evidence, the judge considered it, the judge came to his conclusion.
"We think that the press shouldn't have a second bite of the cherry trying to lobby ministers again with arguments that failed in front of the public inquiry."
"What concerns me is the parasitical elements within the press who abuse their position in here (Parliament) in terms of hiding behind their pen and calling people names," he said.
"That's the so-called brave people. I don't understand why they are allowed to come into this place and behave in the way that they do."
Posting on Twitter on Tuesday night, Rupert Murdoch appeared to suggest the Queen could block the mooted regulation system.
"UK Royal Charter requires Queen's signature. Unlikely without full all party support. Queen doesn't do politics," he wrote.