Late last night, the Transport Agency said contractors working to clear the road had almost broken through one of the slips, but it was still raining heavily.
Spokesman Ewart Barnsley said the main priority was to get the vehicle occupants out.
He said the agency did not believe the trapped people were in any danger.
As the storm band moved across the west of the South Island, police in mid-Canterbury warned people to evacuate low-lying areas along the Rakaia River because of fears rising waters could breach the river banks.
The warning was withdrawn late last night.
It came after a day in which three of the South Island's main tourist routes were closed, disrupting the plans of hundreds of holidaymakers.
The main casualty was the single-lane bridge over the Wanganui River near Harihari on the West Coast, part of which was washed away.
Mr Barnsley said about 40m of highway was "gouged out" by floodwaters.
As the bridge came apart, it severed a cable that provides internet and phone services - including 111 calls - to Harihari, Fox Glacier, Haast, Franz Josef and surrounding areas.
Meanwhile, 120 Milford Track trampers arrived in Milford Sound yesterday after spending an extra three days in Department of Conservation huts.
The track was closed when more than 400mm of rain lifted rivers to dangerous levels.
DoC official Annie Wallace said water on some parts of the Milford Track would have been well above trampers' heads.
"This was by far the biggest flood we have seen."
Weatherwatch analyst Richard Green said the Haast Pass and Arthurs Pass roads had been closed by floods. The Lewis Pass remained open, but there were severe gales in some parts.
Mr Green said northwesterly gales ripped through inland areas, exceeding 120km/h and reaching 140km/h around the divide.
The weather sent temperatures plummeting. Alexandra yesterday reached 11C - the coldest the town has been on January 2 - and popular New Year spot Queenstown's highest temperature was 13C.
MetService forecaster Andy Downs said the rain was easing in Westland, but a heavy-rain warning had been issued for north-west Nelson and Buller, and a band of thunderstorms had also been triggered.
"They could increase the rain rates up towards the torrential levels, 40mm plus per hour. If that happens, you can start getting flash flooding on top of everything else."
But the front would ease as it moved up the country, Mr Downs said.
"The good news is there's a ridge of high pressure following in behind this, and that is set to sit over central New Zealand right until Sunday.
"So once this front has cleared the country [this] morning, we're looking at an improving trend."