Kristine Klugman was diagnosed with bowel cancer in 2011, and an operation wasn't possible.

She is now in remission. But her six weeks of chemotherapy was "a long and painful business", and if it had gotten any worse, she says she would have ended her life.

"I can quite understand people getting to that point, and deciding that really, they've had enough," she says.

Dr Klugman is a strong advocate for euthanasia, or assisted dying.

If she lived half an hour east of her Canberra home in the country New South Wales town of Queanbeyan, she would be able to have a say on whether it should be made legal.

But because she lives in the ACT, she does not have that right.

Why is it different in the territories?

The Northern Territory and ACT governments can legislate on abortion, medicinal cannabis and other sensitive medical issues, but have been prevented from making laws on assisted dying for two decades.

In 1995, the NT became the first place in Australia — and one of the first jurisdictions in the world — to pass euthanasia laws.

Four people used the laws to end their lives before Liberal MP Kevin Andrews put forward a bill to ban the territories from making their own laws on the matter, which passed on a conscience vote.

It means the Commonwealth Parliament has the constitutional power to step in and overrule them.

Today, the Senate considered Liberal Democrat senator David Leyonhjelm's bill to overturn that ban.

But that failed, with the bill losing 36 to 34 — meaning the ACT and NT will continue to have no right to legalise assisted dying.

Dr Klugman wants the ban gone. She says it is "illogical" and makes her feel like a second-class citizen.

Territory politicians have more mixed feelings about it.

Senators voted on their conscience, not along party lines, and Senator Leyonhjelm earlier said he was confident the bill he put forward three years ago would this week pass the Senate after three days of debate.

So what do those in power say?

Not all Territorians are behind the push to restore their rights.

ACT Liberal senator Zed Seselja says checks and balances in a democracy are important.

"They don't necessarily want their local assembly and 13 members of their local assembly to have absolutely unfettered power," he says.

Senator Seselja says if assisted dying were legislated in the ACT, it would have national implications.

Zed Seselja supports territory rights but warns that legalising assisted dying in the ACT would have national implications. ( ABC News: Jake Evans )

And while his ACT counterpart, Labor senator David Smith, will vote to scrap the ban, he too has expressed reservations around euthanasia legislation itself.

Up north, Labor senator Malarndirri McCarthy and Country Liberal senator Nigel Scullion are in lockstep: they want Territorians to have the same right to decide as the states.

Senator McCarthy says Territorians have the right to make their own decisions.

"What gives you the authority, the moral authority ... to think that your ability is much better and greater than theirs?" she told the Senate during a late-night debate on the issue this week.

NT senator Malarndirri McCarthy wants Territorians to have the same rights as those in the states. ( ABC News: Matt Roberts )

And ever since his first days in Parliament, Senator Scullion has been vocal on Territory rights.

In his maiden speech, he brought up the ban as an example of Territorians being given "little input" in determining their own future.

"Territorians' very mature attempt to resolve the most complex of social issues was treated with contempt, and our decisions were overturned as if we were errant children," he said.

Dr Klugman says she can't explain why this constitutional power would be used on euthanasia issues for Territorians.

"It's treating them separately and differently, and it's just not just," she says.

Senator Seselja acknowledges it's a cause of frustration for many Canberrans, but says ultimately "that is part of our history and the way we were created".