However, he said those that could not get in would not get paid.
"Our normal policy is that if you are not able to work a shift you are not paid for it, but what we do is provide our colleagues with the opportunity some time in the following month to make those hours up at a time that suits them," he told the BBC.
On Wednesday, all Sainsbury's stores were open and all deliveries were made, and Mr King said he expected that to be the case on Thursday, though he admitted some deliveries might be delayed.
There had been a little bit of panic buying, with some customers stocking up on canned goods, but on the whole people had been "pretty sensible", he said.
Richard Hunter, head of UK equities at Hargreaves Lansdown Stockbrokers, said while the trading update was "impressive", there remained a number of concerns for investors.
"Sales were above expectations, and sliced in different ways there were signs of a very robust performance," he said.
"However, the company also echoed the doubts expressed by most other consumer facing businesses at the moment regarding the challenging nature of the consumer horizon."
Other retailers have also warned about the prospects for 2010, despite reporting strong Christmas trading.
On Tuesday, John Lewis reported record sales for the Christmas season, with like-for-like sales up 12.7% in the five weeks to 2 January at its department stores. However, it said this performance was unlikely to be sustained.
On Wednesday, Marks and Spencer reported a 0.8% rise in UK like-for-like sales for the three months to Boxing Day.
M&S chairman Sir Stuart Rose said the firm had seen a "good Christmas", but added that trading in 2010 would be tough.
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