The Tories have been dealt a huge blow as new figures show the government missed its targets for accident and emergency waiting times in England, which have hit their worst level for a decade.
Just 92.6% of patients were seen at A&E within four hours from October to December, NHS England records show, falling short of the government target of 95%.
But health secretary Jeremy Hunt said maintaining patient safety was more important than meeting targets.
Mr Hunt admitted there is a "huge amount of pressure" on the NHS in England and hospital bosses feel they are "running just to keep still" to cope with rising demand.
"We want to do better than that, and we want to do everything we can, but what we don't want to do ... is for trusts to make compromises, as has happened in the past, on patient safety, on compassionate care, just in order to hit the targets.
"Targets matter, but not at any cost."
Hunt stressed to the BBC Radio 4 Today programme that nine out of 10 patients were being seen within four hours, which was "better than any other country in the world".
The pressure on hospitals has led to a number of trusts declaring major incidents in order to cope with a surge in patients.
Mr Hunt said: "There is a huge amount of pressure, that's absolutely clear."
But he added: "I think we also have to recognise, despite the particular pressures, despite the major incidents - and you always get some major incidents at this time of year - that the NHS is continuing to see in A&E departments nine out of 10 people within the four-hour target.
"That is actually better than any other country in the world that measures these things."
The Health Secretary said "some progress" was being made in recruiting more clinical staff, but he acknowledged the frustration felt by those running hospital trusts.
"Although capacity is expanding, there is a sense of running just to keep still because the demand at the front door continues to increase at an even greater rate," he said.
Mr Hunt's Liberal Democrat colleague, Norman Lamb, admitted the NHS "is not meeting" its targets,
Speaking to ITV's Good Morning Britain, Mr Lamb said Britain's ageing population means hospitals are having to treat older patients with chronic conditions.
He said: "We rightly have the toughest targets in the developed world. We are not meeting them.
"We are living longer, the pressures of people living with chronic conditions. We hear lots of reports from A&E departments of older people particularly turning up more ill than they have in the past."
A surge in demand at emergency departments has forced several hospital trusts to activate major incident plans.
Gloucester Royal, Cheltenham General Hospital, Scarborough Hospital and the University Hospitals of North Midlands in Staffordshire have implemented the emergency measure.
Others, including the Royal Surrey County Hospital urged people to stay away from A&E unless their case was a genuine emergency.
Mr Hunt said the changes set out by NHS England's Simon Stevens could help address the problems in the health system.
"In the last six months something very big has changed, which is that the NHS itself has lifted up the bonnet on this problem and looked at the heart of the issue and come up with its own plan to deal with it.
"It was put together by NHS England by Simon Stevens, the new chief executive, and the Government in the Autumn Statement - because it costs money - agreed to fund it, and we can do that on the back of the strong economy, that is possible because of the difficult decisions that have been made.
"I don't want to say that's a silver bullet but I think that is a sense of progress."
Mr Hunt said changing the way elderly people were treated in the health service was crucial to easing the pressure on hospitals.
He said: "The incentives aren't right. Let's look at the heart of this: the real issue is the way that we look after the most vulnerable and frail older people.
"At the moment all the incentives are to treat them in hospitals, and that is causing hospitals to fill up."
The president of the College of Emergency Medicine said the pressure on staff was "intolerable", with around 20,000 more patients a week attending A&E than a year ago.
Dr Clifford Mann said: "We have reached a tipping point - 20,000 extra patients a week all have to be accommodated within the same bed stock and the same capacity as the system in 2013."
He told BBC Radio 4's Today programme: "The thing that concerns me is this daily, weekly intolerable pressure is starting to have an effect on staff. They are more likely to become sick, they are more likely to be unable to work and they burn out and choose to go into other professions.
"That means this is not a sustainable situation."
He highlighted a shortfall in recruitment for A&E roles: "There is a 50% vacancy rate for the last three years of training. We recruit well into year one because emergency medicine is a very professionally rewarding career, but by the time they get to year three, 50% choose either to choose a different specialty or to emigrate.
"So there are now 500 UK-trained emergency doctors working in Australia which cost the British taxpayer a quarter of a billion pounds to train."
Sustainable staffing levels "will only happen when we stop penalising acute trusts" because "the current tariffs mean that you can run a successful, indeed profitable, hospital if you do specialist commissioning work in elective care, but all acute care loses money".
He added: "In times of austerity, it's difficult for trusts to invest properly in an emergency department which they see as a loss-making part of the business."
Mike Proctor, deputy chief executive of York Teaching Hospital NHS Foundation, which is responsible for Scarborough Hospital, also highlighted difficulties in recruiting staff in the UK.
He told Today: "They do not exist, that's the major problem at the moment, they do not exist. We are about to, as an organisation, go out to Spain next month to actually recruit some nurses from Spain."