"That's our goal at this moment," said utility spokesman Brent Staeben.
About 150 customers may have to wait until Friday to be reconnected, he said.
"Those are folks who live in some harder-to-get-to areas, particularly in Charlotte County. We're actual moving on Morooka and snow machine to get into some of these particular outages."
Seasonal homes are also expected to have power restored once other customers are reconnected.
The bulk of the latest outages are in the Woodstock area, with nearly 2,600 customers affected.
Customers in Fredericton, St. Stephen, Sussex, Rothesay and Quispamsis are also waiting for heat and lights to be restored.
More than 250 line and tree-trimming crews are working round the clock.
Some blame lack of tree trimming
Still, in Quispamsis, at the Terrace View Community, where mobile home residents like Norine Bartlett have been without power for more than a week, patience is running thin.
"We're running a generator that costs $80 a day. Our money's getting low. What are we supposed to do?" asked Bartlett.
One of her neighbours is using rent money to buy fuel, she said.
Tom Gribbons, who has also been without power at his Rothesay home for about a week after tree branches crushed the nearby power lines, contends it could have been prevented.
"I put a call into NB Power last summer asking them to trim some trees. And the response that I received was, 'We don't do that anymore.'"
NB Power officials deny any cutbacks. They say they have maintained a substantial tree-trimming program over the past few years and have had a budget increase approved for 2014.
Rothesay Mayor Bill Bishop says it's not enough. "Tree maintenance must be stepped up," he said.
Liberal Opposition Leader Brian Gallant has also questioned the lack of regular tree-trimming around power lines and said he plans to question the Alward government's response to the widespread and lengthy outages once the legislature resumes in February.
Health Minister Ted Flemming says the government is not to blame.
"The fact of the matter is it was an unprecedented storm," even worse than the storm of 1998, said Flemming, who went without power for six days at his Rothesay home.
"This storm resulted in New Brunswick Power losing 25 per cent of its residential customers."
People need to put the situation in perspective, said Flemming.
"I spend a lot of time dealing with hospitals, which have sick people and I think we would all do well to say if the biggest problem you have on Christmas Day is that you don’t have electricity — well, I think there’s a lot of hospitals you could go to and I think people would say, ‘I think you’re doing just fine,'" he said.
"There was no incident whatsoever of lawlessness, or looting, or police being called, or anything else like that," stressed Flemming. "In terms of any severe human tragedy, it has been remarkably silent in that area.
"So there’s going to be the naysayers, and there’s going to be some person who’s going to go on and want to blame somebody — somebody should have done this and somebody should have done that and how did the government let this happen. But the great story here is to see the people of New Brunswick come together in such difficult times."
Warming centres remain open in some of the hardest hit areas, but some have scaled back to daytime hours, including the locations in Grand Bay and Quispmasis.
The Quispamsis centre closes for good at 4 p.m.
On the Kingston Penninsula, the Anglican Parish hall at Kingston Corner remains open. The Red Cross is staffing warming stations in St. George at Magaguadavic Place on Spinney Drive, and in Oak Bay at the local fire department.
In the past week, about 82,000 homes and businesses have been without electricity at some point, NB Power officials have said.
Some customers have been without power for more than a week. In some cases, customers have lost power six times.