NSW opposition leader Jodi McKay wants the border between her state and Victoria shut immediately.
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A surge in cases from hotel quarantine in NSW and the start of the school holidays in the state prompted Ms McKay's call for a hard border closure.
Such a move would create mayhem for border towns such as Albury-Wodonga.
"NSW and Victoria must work together and as all options are considered, prudent and reasonable arrangements will be needed for our border communities," the state Labor leader said.
"Until now I have supported the Premier's decision not to change NSW-Victoria border arrangements.
"But school holidays are now underway and the NSW Government's actions so far to prevent infectious arrivals in our state have been inadequate.
"The NSW Premier has steadfastly refused to re-examine border arrangements as the Victorian situation worsens.
"However a closure needs to be considered and on the table while the spread is not contained."
There were 14 coronavirus cases reported in NSW on Sunday and all were overseas travellers in quarantine in Sydney.
Albury councillor and Labor Party member Darren Cameron disagreed.
"I don't agree with it. It is impractical," he said.
"If it were to be done arrangements would have to be put in place for communities along the river such as Albury-Wodonga where a large portion of residents live in one state, but work on the other.
"I'm also worried about fire affected communities, many of whom are relying on visitors in these school holidays to get their economies up and going again."
NSW has presently shut its border to residents from Melbourne virus hotspot postcodes which were expanded at the weekend.
Albury mayor Kevin Mack said the council was in contact with member for Albury Justin Clancy's office on the issue.
"Whilst it would not be ideal, we will be guided by the Chief Medical Officer's advice and the Premier's department," he said.
"We are all in this together and need to do what is necessary to avoid further outbreaks in NSW and more importantly our border communities."