Rishi Sunak has been accused of making a “political choice” to allow patients to die unnecessarily.
In a statement on Monday, the British Medical Association (BMA) said the future of the NHS was “balanced on a knife-edge”.
It comes amid warnings that the deaths of up to 500 people each week could be caused by delays in emergency care.
More than a dozen NHS trusts and ambulance services declared critical incidents over the festive period.
The Lib Dems have demanded parliament - which is not due to sit until next Monday - be recalled so MPs can discus the crisis.
Phil Banfield, the chair of the BMA, said the current situation in hospitals was “intolerable and unsustainable”.
“It is disingenuous for the prime minister to talk about ‘backing the NHS’ in his New Year message, when his own health secretary is failing to discuss how this crisis can be fixed,” he said.
“Instead of criticising frontline doctors, nurses and paramedics for wanting to be valued and given the facilities to provide treatment and care, the government should deliver on its obligations to the public.”
The BMA, the trade union and professional body for doctors and medical students in the UK, added: “It is just not true that the cost of resolving this mess cannot be afforded by this country.
“This is a political choice and patients are dying unnecessarily because of that choice.
“The government must step up and take immediate action. Without intervention, waiting lists will continue to grow, patients will continue to suffer, and staff will continue to leave.
“The future of the NHS is balanced on a knife-edge; it is solely within Government’s gift to pull this back from the brink.”
Education minister Robert Halfon told the same programme the pressure on A&E departments was a “top priority” for the prime minister.
Earlier, the Royal College of Emergency Medicine (RCEM) doubled down on its claim that somewhere between 300 and 500 people are dying each week as a result of delays and problems with urgent and emergency care.
Ian Higginson, the vice chair of the RCEM, told BBC Radio 4′s Today programme: “If you’re at the front line, you know that this is a longstanding problem.
“This isn’t a short-term thing. The sort of things we’re seeing happen every winter, and it still seems to come as a surprise to the NHS.”
Last week, one in five ambulance patients in England waited more than an hour to be handed over to A&E teams.
NHS trusts have a target of 95% of ambulance handovers to be completed within 30 minutes, and 100% within 60 minutes.
In November, 37,837 patients waited more than 12 hours in A&E for a decision to be admitted to a hospital department, according to figures from NHS England.
This is an increase of almost 355% compared with the previous November, when the figure was 10,646.