Several Tory MPs have expressed unease about the decision to ring-fence the NHS from government spending cuts.
Nadine Dorries, a member of the Health Select Committee, told the BBC's Politics Show it was "untenable" as other departments faced 25% cuts.
Former chancellor Lord Lawson said the commitment was "understandable" but he did not believe it "would wash".
But Treasury Chief Secretary Danny Alexander said the NHS was one of the services that "everyone relied upon".
He stressed that the NHS would be expected to find efficiency savings so that money could be invested in better health care.
Under coalition plans, only health and international aid will be protected from spending cuts to be decided this autumn, with other departments facing average real terms cuts of 25%.
Ministers are already under pressure to find further savings in the welfare budget in order to minimise the impact of cuts on areas such as schools and the police.
The Conservatives made the pledge to guarantee a real terms increase in NHS funding before the election, David Cameron describing the health service as his "number one priority".
He said an ageing population and the need to provide money for new drugs and technology were among the reasons for safeguarding health service funding.
But several Tory MPs have said the commitment is unrealistic given the financial climate and should be rethought.
"I don't think it is tenable to accept the NHS budget should be ring-fenced or increased," Nadine Dorries said.
"I think we need to find the political courage to accept there is excessive waste in the NHS and it is unfair to expect the other department to take all the hits."
Conservative colleague Brian Binley said he was "really concerned" about the pledge in light of the "sizeable" budget cuts other areas were likely to have to accept.
"We ought to be able to do away with ring-fencing with that money coming back to the central part to feed the vital services that are being cut so drastically."
Lord Lawson said his party had been desperate to establish its credentials on the NHS in the face of opposition claims that it would preside over its "destruction".
"It is understandable to see why they said it. But I think it won't wash, it won't work."
At the general election, senior Liberal Democrats, including Vince Cable, also spoke out against ringfencing the health budget.
But Danny Alexander, the man responsible for agreeing budgets with individual departments, said he believed it was the "right thing to do".
"The health service is one of the public services which everyone in this country more or less relies on," he told the BBC's Politics Show.
A small real terms increase in spending would still be "tough" for the NHS, given the "financial pressures" on it, he added.
"Of course, we will be seeking the same sorts of efficiency savings in the NHS and progress on making savings across the board so that money can be invested in the health system."
And the government was defended by veteran backbencher John Redwood, who has queried other aspects of the coalition's programme such as the rise in capital gains tax.
"We, like the other parties in Britain, believe in health care free at the point of need," he said.
"If you are going to meet that pledge, you have to provide the money for it."