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16 December 2014 Last updated at 08:58 GMT
Dr Andrew Goodall said a choice may have to be made between emergency care and non-urgent surgery.
In an extended interview with BBC Wales health correspondent Owain Clarke, Dr Goodall said hospitals might make the decision not to schedule surgery in the first place to focus on "front door pressures" during the peak winter months.
Two hospitals, Morriston in Swansea and the Princess of Wales in Bridgend, have already cancelled some surgical procedures until after Christmas.

Aiden Webb, 22, from Norwich, was climbing Fansipan mountain alone on Friday when he fell down a ravine and lost his way, his girlfriend Bluebell Baughan said.
Mr Webb, described as an experienced climber, was last heard from on Saturday when his phone went dead.
The Foreign Office confirmed it was assisting his family.
Mr Webb and Miss Baughan were on a four-month trip when he injured his arm and knee in the fall on the 3,100m (10,300ft) high Fansipan mountain in the north of Vietnam.
More on this and other stories from Norfolk
"He went to the mountain alone without a guide at 06:00 and aspired to climb it in one day," Miss Baughan said.
She was in touch with Mr Webb by phone when he informed her he had fallen and could not find his way back to the trail.
"He was sure he could make it back but by nightfall it was apparent he wasn't going to," she said.
"Aiden said a rock had cut his arm open and he had hurt his knee. We were in touch all night.
"He said no-one would be able to find him, but by 6am on Saturday he finally agreed to me getting help."
Miss Baughan, who is helping co-ordinate the search from the town of Sa Pa, said rescuers had been on the mountain since Saturday morning.
"Thirty-two men spent last night on the mountain, a mixture of military police, forestry workers and local police.
"There is only one police officer here in Sa Pa who speaks English, but everyone has been very helpful," she said.
Miss Baughan said conditions on the mountain were "very cold and wet".
"Aiden is a very good climber, but he is injured," she said.
Mr Webb's father and uncle are expected to arrive in Vietnam this evening although they will not reach the north until Tuesday.
A Foreign and Commonwealth Office spokeswoman said: "We are supporting the family of Aiden Webb, a British man reported missing in Vietnam. We are working closely with the local authorities leading the search."

Walker was a passenger in a Porsche a friend was driving when it hit a pole and burst into flames in November 2013.
US media report that a wrongful death case has now been filed by Walker's daughter Meadow, who is 16, alleging the carmaker took safety shortcuts.
Porsche has not yet publicly responded to the claims.
After a four-month investigation, police said the Porsche Carrera GT, driven by Walker's friend Roger Rodas, was travelling at 94mph (151kph) in a 45mph zone when it hit a lamp post.
The lawsuit contends that the car was travelling much slower when it went out of control, according to TMZ.
The website, quoting legal documents, says his seatbelt "snapped Walker's torso back with thousands of pounds of force, thereby breaking his ribs and pelvis," and trapping him when the vehicle caught fire.
According to the Los Angeles Times, the document claims the car lacked "features that could have prevented the accident or, at a minimum, allowed Paul Walker to survive the crash".
Meadow Walker has not commented.
Mr Rodas' widow filed a similar case last year, but Porsche said the crash was his fault, rather than down to design flaws.
The new chief executive of the Welsh NHS has told BBC Wales winter pressures could force hospitals to cancel operations.
[NEXT_CONCEPT]
A British man is missing in Vietnam after falling while attempting to climb the country's highest mountain.
[NEXT_CONCEPT]
The daughter of the late Fast and Furious actor Paul Walker is to sue carmaker Porsche over the crash in which he died, US reports say.