There are pleas for the prime minister to call a cross-party review of the health and social care systems.
Chairs of three influential House of Commons committees have written to Theresa May to say that political consensus was needed to find a long-term solution to the "pressing" social care challenges facing the country.
The trio - Conservative MP Sarah Wollaston of the Health Committee, Labour's Meg Hillier of the Public Accounts Committee, and the Communities and Local Government Committee's Labour chair Clive Betts - called on Mrs May to invite all parties to take part in an "urgent" review.
They want to examine the financial sustainability of the social care system and the NHS, to be completed in time for an agreed approach to be reflected in the next Government spending round.
The letter came two weeks after the three chairs directly addressed Mrs May on the need for a review during her appearance before the Commons Liaison Committee on December 20.
Mrs May agreed then that previous governments had "ducked" the issue of social care funding and said she was determined to ensure a sustainable system for the future.
She said that it would be "for everybody to contribute and to be part of that decision", but appeared to pour cold water on the idea that the best way to ensure consensus was a cross-party review, telling Dr Wollaston: "Past experience does not suggest that that is the case."
In their letter, the three MPs told Mrs May: "We were encouraged by your recognition at the Liaison Committee that everyone has a part to play in finding a sustainable way of ensuring social care provision in the future. You also accepted the need for a review to find a way of funding social care sustainably for the long term.
"We believe that can best be achieved if there is cross-party consensus, and therefore urge you to invite all parties to become involved in a review, which should begin as soon as possible.
"Given the scale of rising demand, this immense challenge will face whichever party is in government over the coming decades."
Chris Ham, chief executive of health think-tank The King's Fund, said the "threadbare" social care sector was facing a £2.4 billion funding gap, while planned increases in health funding were "not enough to maintain standards of care, meet rising levels of demand, and transform services".
"A new settlement for health and social care is long overdue," said Professor Ham.
"For too long there has been a lack of political leadership on these issues. We agree with the committee chairs that a political consensus that puts health and social care funding on a sustainable footing is sorely needed. Without a consensus, patients and people in need will suffer."