Culture secretary Maria Miller has expressed hope that a cross-party deal on press regulation could still be struck ahead of a showdown in the Commons.
But according to Politics Home Ed Miliband will not accept David Cameron's plans for a royal charter on press regulation and will go ahead with the vote.
MPs are due to decide tomorrow on the shape of a new watchdog system to meet the demands of the Leveson Report into phone-hacking and other abuses.
Labour and the Liberal Democrats have joined forces to propose a regulator set up by royal charter and underpinned by legislation.
The Conservatives also propose a royal charter but Miller said any move to back it in statute could have a "chilling effect" on free speech.
But with David Cameron facing likely defeat in the Commons after pulling the plug on cross-party talks, there were signs he was willing to compromise.
"I hope that the discussions that we have over the next 24 hours can really make sure that we can come together and have a real solution here," Miller said.
"We can have tough self-regulation of the press with million pound fines, prominent apologies, without having the potentially chilling effect that statutory underpinning would bring."
She spoke after George Osborne also indicated a desire for agreement, telling the BBC: "There is still an opportunity for us to get together and get a press law that works."
Political disagreement over the solution was a recipe for regulation that would not last or become "deeply-rooted in our culture", he said.
Cameron - who has said he will stand by the vote - yesterday said he did not consider the Lib/Lab proposed statutory underpinning "a big issue of principle".
Labour said it had not had any approach for fresh talks, however, and would remain "resolute" in pushing for tough controls tomorrow to protect victims of press intrusion.
Shadow culture secretary Harriet Harman said the party had "always said we would like to reach agreement" which could be brought to the Commons as a united position.
"There are just a few issues that remain between us, but they are quite important ones," she told Sky News.
With up to 20 Tories reportedly ready to back the Lib/Lab pact, allies of Cameron accept he will be hard-pressed to win the Commons vote despite intense efforts to shore up support.
Tory former Cabinet minister Lord Fowler encouraged the party's MPs to rebel as the Lib/Lab plan "comes closest to implementing Lord Justice Leveson's careful and objective report".
Cameron insists he is acting as "a friend of the victims" of phone hacking, but one of them, author JK Rowling, said they had been "hung out to dry" by the Prime Minister.
"I am merely one among many turning their eyes towards Ed Miliband and Nick Clegg and hoping they have the courage to do what Cameron promised, but which he failed to deliver," she said.
Miliband urged MPs to do their "duty" by her and others such as the parents of murdered schoolgirl Milly Dowler and disappeared Madeleine McCann.
"We are at this moment which is a sort of crossroads: do we change or is it more of the same? We need to choose the right course, and I think it is a test of politics," he told The Observer
Actor Hugh Grant, who fronts the Hacked Off campaign, said the royal charter plan was not "ideal" but said victims supported it and urged Tory MPs to defy Cameron.
"MPs promised victims to do right by them and they have that chance on Monday," he said.