Nationals deputy leader Perin Davey told The Canberra Times that the ACT Legislative Assembly shouldn't be banned from debating the issue.

"I would support the territory rights bill going through," she said.

"As a former resident of Canberra, I just think it's right that the ACT has the opportunity to debate their own rules."

Senator Davey is the third Coalition senator to confirm she'll support Alicia Payne and Luke Gosling's territory rights bill, following public declarations from Liberals Simon Birmingham and Andrew Bragg.

The private members' bill last week comfortably passed the lower house 99 votes to 37.

Opposition Leader Peter Dutton and Nationals leader David Littleproud used their free vote to support the bill, but were in the minority among Coalition MPs.

The vote is expected to be much tighter in a traditionally more conservative-leaning Senate, which is where the fate of the so-called Andrews bill will be decided as soon as next month.

The final vote could hinge on the number of yes votes from Coalition senators, given a number of Labor upper house members are likely to vote against the bill because of personal objections to voluntary assisted dying.

Four of the seven Labor senators who helped sink David Leyonhjelm's territory rights bill in 2018 - Don Farrell, Helen Polley, Pat Dodson and Deb O'Neill - remain in parliament.

Labor figures, including ACT senator Katy Gallagher, will spend the coming weeks lobbying their upper house colleagues ahead of a vote.

While Mr Gosling was hopeful the bill would be debated as soon as parliament reconvenes on September 5, supporters are cautious not to rush the process and potentially derail its success.

The Senate debate is likely to take far longer than what was needed before it passed the House of Representatives on Wednesday morning.

Sources are pointing to the conscience vote on mitochondrial donation in the last parliament, where debate ran for 20-odd hours, as an indication of what could be in store for the territory rights bill.

MORE OUR RIGHT TO DECIDE CAMPAIGN

That could create a scheduling headache for the government, which has a large legislative agenda - including its signature climate change bill - that it wants to deal with.

Senator Gallagher on Friday said she expected the upper house vote to be much tighter, as she conceded some of her Labor colleagues would vote against the bill.

Five Labor MPs voted against the bill in the lower house, including Leader of the House Tony Burke and Veterans Affairs Minister Matt Keogh.

Senator Gallagher said she wanted her colleagues to treat the bill as a matter of territory rights rather than assisted dying, but acknowledged that it was difficult to separate the two for those with strong views.

"I'm optimistic [that the bill will pass], but I think it'll be a lot closer in the Senate," she told ABC Radio.

"And for those of us that are campaigning for the passage of this bill, I think we've got a fair bit of work to do to talk to all of our other Senate colleagues to encourage them to support the bill.

"But I am optimistic, but I think there's some more work to do."

The Canberra Times has been calling for a repeal of the Andrews bill as part of its year-long Our Right to Decide campaign.

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