Boris Johnson is expected to make a final decision over the weekend about whether to press ahead with his controversial social care funding plan, in the face of a growing backlash from cabinet ministers and backbench MPs.

One government source described “chaos” in a jittery Downing Street on Friday, after leaks about plans for an increase in national insurance contributions (NICs), including the contested claim that the health secretary, Sajid Javid, has been demanding a rise of two percentage points.

It is understood Johnson still hopes to announce the package next week, but several cabinet ministers are privately fuming about the idea of a manifesto-busting tax rise that will hit young adults on low incomes, but leave pensioners unscathed.

Backbench Conservative MPs including Jeremy Hunt and John Redwood went public with their concerns about an NICs rise on Friday.

Hunt told BBC Radio 4: “Since older people are the biggest beneficiaries, it’s fair they should make a contribution.”

Another Conservative backbencher said Johnson could even struggle to get the measure through a restive House of Commons. “People have been through enough, and we should focus on getting the economy going again. Yes, social care is a ticking timebomb, but does it have to be right now?”

They added: “It just doesn’t feel very Conservative, especially given the manifesto pledge.”

Johnson’s former chief aide Dominic Cummings waded into the row, calling an NICs increase “bad policy and bad politics”.

“Why should young people on average and below-average incomes lose disposable income to pay for another subsidy for the older middle classes?” Cummings asked, in the latest posting on his £10-a-month Substack site. He predicted Johnson could yet succumb to political pressure and “trolley” away from the plan.

Another Conservative MP said he believed colleagues would reluctantly support the proposal, however. “This is a tax rise, specifically on people who work, so MPs are massively torn, but most people will think, given the pressures on the NHS, let’s just bloody do it,” they said.

Depending on the outcome of discussions about how much funding is needed, the proposal is expected to include an increase of 1 or 1.25 percentage points in NICs – badged as a “health and social care levy”.

For someone on average earnings of £29,536 a year, an increase of one percentage point would cost them £199.68 annually.

The proceeds would be devoted to relieving Covid pressures on the NHS in the early years of the plan, with more resources flowing to social care as time goes on.

The proposal is expected to include a lifetime cap on the costs an individual will have to pay towards their care, as originally recommended more than a decade ago by the Dilnot review, commissioned by David Cameron’s government.

Officials in Downing Street are said to be fretting that while the political costs of a tax increase will be high, even a 1.25-percentage-point rise will fail to fix the crisis in social care, or tackle the Covid backlog in the health service.

One source suggested the prime minister had been angered by the suggestion that even after the tax rise, it could take a decade for the NHS to return to pre-pandemic performance.

The chancellor, Rishi Sunak, is also expected to announce that he will not honour the “triple lock” for pensions this year, with wage increases, which pensions track, artificially boosted by the end of furlough. Sticking to the rule could mean an increase in the state pension of as much as 9% next April.

Politically, hitting pensioners by ditching the triple lock for this year could act as a counterweight to the fact that they will be left unscathed by the NICs rise.

With more than two years having elapsed since Johnson promised he had a plan ready to fix the social care system, the government is keen to have it announced and agreed by MPs in the brief, three-week sitting of the House of Commons before the annual party conferences.

The justice secretary, Robert Buckland, said on Friday that any future social care plan must be “adequately funded”, but that no final decision had been taken by the government on how this was to be achieved.