Labor candidate Michael Holland looks likely to have secured the seat for the party for the first time in its history, in one of four by-elections on Saturday.
Labor also looks set to retain former leader Jodi McKay's Strathfield seat, while the Nationals are on track to retain former deputy premier John Barilaro's Monaro seat. The Liberals will also retain former premier Gladys Berejiklian's Willoughby seat.
The final results could take until March 11 due to a surge in postal votes, which the NSW Electoral Commission will begin processing on Wednesday.
The government rejected suggestions the by-elections were a referendum on its response to the pandemic and the Omicron outbreak, pointing to local issues in the individual electorates.
Treasurer Matt Kean told ABC Radio National the by-elections were not "a referendum on the government".
"These were four by-elections, which had unique issues in each of the seats."
Premier Dominic Perrottet said on Monday he's not concerned about being pushed further into minority government and won't be cutting deals with minor parties and independents on the crossbench, but will work with them on "legitimate areas of policy".
Mr Minns said on Tuesday his party is "very hopeful about the next election" but not overconfident.
"No one in Labor is doing victory dances ... I think it does show that there are Labor voters (in regional electorates), but we have to fight for each and every vote."
"We have not earned a mandate from the people of NSW, we're determined to do it, but we've got 12 months to go," he says.
The lower house of parliament will meet for the first time this year on Tuesday, while the upper house will resume next week.
