The prime minister has received letters from senior ministers raising concerns about the spending cuts after a number spoke out against the measures at Tuesday's cabinet meeting.
Some departments are facing cuts of as much as 20 per cent as Ms Reeves scrambles to find £40bn of spending cuts and tax rises before the October 30 Budget.
She told ministers during Tuesday's Cabinet meeting that plans to fill a £22bn hole in the public finances will be enough only to "keep public services standing still". Having promised "no return to austerity" under Labour, Ms Reeves is seeking the additional £18bn to fund a cash injection for the NHS and avoid real terms cuts to some key departments.
Ministers are said to be directing pushback against the cuts toward Ms Reeves more than the prime minister as she puts the finishing touches on her first Budget. Among those who have written to the PM expressing alarm are his deputy Angela Rayner, justice secretary Shabana Mahmood and transport secretary Louise Haigh, Bloomberg reported. Concerns are said to expand across the cabinet, with particular fear among those outside of health, defence and education whose departmental spending is not "protected".
Asked on Thursday whether she joined colleagues writing to the PM ahead of the Budget, education secretary Bridget Phillipson told Sky News: "We have all had conversations, meetings and correspondence as part of the usual budget process. I'm not going to get into a discussion about meetings or private conversations."
Experts have argued that ministers need to find £20 billion to avoid a squeeze on so-called "unprotected" departments pencilled in by their Tory predecessors, and billions more to prevent a sharp fall in investment spending.
Some of that could come from changing the measure the government uses to calculate debt, but economists from the Institute for Fiscal Studies have suggested that some tax rises are all but inevitable to prevent cuts to day-to-day spending.
The backlash came as it emerged Ms Reeves will use her Budget to increase capital gains tax on the sale of shares and other assets but will not change the rate for second homes.
Capital gains on profits from the sale of shares, which is currently levied at 20 per cent, is likely to rise by "several percentage points", The Times reported, a move which would raise billions. It is also widely expected the chancellor will hike the employer rate of national insurance. An increase in the rate by 1p could raise up to £17bn, according to IFS director Paul Johnson.
But the move would be seen as a breach of Labour's general election manifesto, which promised: "Labour will not increase taxes on working people, which is why we will not increase national insurance." Ministers have argued the promise only applied to the employee rate of national insurance, which sits at 8 per cent, and not the 13.8 per cent employer contribution rate.
Downing Street has denied that Sir Keir gave the public the wrong impression about the scale of tax rises that would come under Labour.
Asked whether the prime minister had misled voters, his press secretary said: "No. So we stand by our commitments in the manifesto, which was fully funded.
"We were honest with the British public, both during the election and since, about the scale of the challenge that we would receive.
Prime Minister's press secretary
"Then, of course, one of the first things the chancellor did when we came in was do an audit of the books and found a £22 billion black hole that the previous government lied about and covered up.
"So that's why we have continued to be honest with the British people that there are going to be difficult decisions in this Budget, and that's because of the mess that the Conservatives left the economy in."