Chancellor Philip Hammond has denied the Prime Minister blocked him from announcing new funds for social care in last month's Autumn Statement.
His comment came as town hall chiefs said they had discussed proposals with ministers to allow hikes in council tax bills in England to fill a black hole in funding for adult social care which could otherwise reach £2.6 billion by 2020.
The Times reported that Theresa May stopped Mr Hammond from introducing the measure in November, but was now giving her backing to changes which could give town halls the freedom to increase the 2% "social care precept" by as much as was needed to solve the crisis.
Labour accused the Government of unfairly "dumping" the funding crisis on council tax-payers and demanded to know why ministers had not "fought harder to get extra, vital funding for social care" in the Autumn Statement.
Mr Hammond told the House of Commons Treasury Committee he had discussed the issue with the PM but insisted it was "not true" that she had barred him from committing more cash.
"We are absolutely aware of the cacophony of input from local authorities and health trusts around the situation in the social care area," he said. "It is an important area and we will continue to discuss it and continue to look at the representations we are receiving."
Meanwhile, Downing Street said some of the blame for the problems in social care were due to under-performing councils.
The worst 10% of local authorities had delays in the transfer of elderly people from hospital into care that were 20 times higher that the best-performing 10%, said Mrs May's official spokeswoman. Half of all delayed discharges are in just 20 local authorities.
A survey last week suggested that council tax payers are already facing inflation-busting rises of up to 4% on bills for 2017/18, around half of which is accounted for by the social care precept.
But the chair of the LGA's community and well-being board, Izzi Seccombe, said local authorities were under pressure from cuts in government grants totalling more than 40% since 2010 and were facing a £600 million bill for the higher minimum wage.
The Conservative councillor told the BBC Radio 4 Today programme: "We need an injection now, we need £1.3 billion now because there is a shortfall by the end of 2020 of £2.6 billion."
The Times reported that ministers were considering giving councils more freedom to increase the precept in the provisional local government finance settlement for 2017/18, which is due to be announced by Communities Secretary Sajid Javid by December 20.
And Ms Seccombe confirmed: "We've had some dialogue with ministers about this and the concern for us is the ability for this to actually fill the gap that we have for long now said that there is in social care."
In an urgent question in the Commons, Labour care spokeswoman Barbara Keeley said allowing local authorities to increase the precept would only widen inequality between rich and poor areas.
"This crisis in social care has been made by this Government, due to £5 billion being cut from adult social care budgets," said Ms Keeley.
"Is it the minister's intention to support a solution that widens inequality of access and denies social care to hundreds and thousands of vulnerable older people?"
Health minister David Mowat replied that councils with better integrated health and social care had far fewer delayed transfers.
"Any system would benefit from higher budgets, and social care is no exception," said Mr Mowat. "But quality matters too."
The PM's spokeswoman dismissed talk of council tax hikes as "speculation" and insisted that the Government had "a strong track record of giving the health and social care system the funding it needs to address the challenges it has faced".
"We now have one million more people over 65 than in 2010, putting pressure on the social care system," she said.
"We know that money alone is not the solution and many councils are providing high-quality social care services within existing budgets.
"This isn't just about funding, this is also about how we deliver an effective and efficient social care system. We do think there is a significant variation in how well councils manage social care services."
Ministers have been warned that any attempt to fill shortfalls in social care funding through the council tax would favour richer areas with a higher tax base, creating a "postcode lottery".
Tory former health secretary Stephen Dorrell said he was in favour of a hike in the precept as a step in the right direction but warned that "people will suffer" without wider change.
And Martin Green, chief executive of industry body Care England, said there were "serious problems" about how money raised from the precept reaches the front line and warned that some companies would "definitely" go bankrupt unless matters improved.
The care sector was now at a "tipping point", with research suggesting that "about 40% of care services will no longer be viable in the medium term", he said.
Liberal Democrat health spokesman Norman Lamb accused the Government of "lurching from crisis to crisis" and described the mooted council tax hike as "yet another desperate sticking-plaster solution which falls short of what is needed".
Mr Hammond acknowledged that a "substantial increase in funding" for social care announced by his predecessor George Osborne was "back-end loaded" so the bulk of the money would reach councils towards the end of this Parliament, which is due to run until 2020.
"We recognise that local authorities are challenged to deal with that profile," he told the Treasury Committee.
But he added that councils had between them added a total of £9 billion to their reserves since 2010.
And he said: "The local authorities will have to look at how they manage this situation to get from here to the very substantial increase across the funding that will be available to them later in the Parliament."
Mr Hammond said it was "clear" from the varying performance of councils in different parts of England that "money alone is not the issue, it is about effective co-operation and collaboration between the NHS and social services".
He added: "The key to this is getting the very best practices that we have seen in some areas rolled out much more widely across England to deliver the kind of high-quality social services we want to see."
Asked why he had not dealt with social care in the Autumn Statement, Mr Hammond said the issue was being handled by the health and communities secretaries, telling the Treasury Committee: "We will all have to get used to a world in which chancellors don't necessarily do everything."