In this age of celebrity, Jacqui Lambie fits the narrative to a tee in the political sphere. She’s a rough-talking woman with a struggle-town back story who has landed centre stage because she has a lot of power – and sometimes the crucial vote – on contested issues in the Senate.

You get the impression Lambie loves both the drama and the influence. She revelled in getting the government to deliver big money to obtain her vote on the tax relief legislation. With chutzpah, she later lamented coming cheap.

But soon Lambie will face a decision with more complexities than tax cuts, affecting relatively few lives but those lives in a huge way. As things stand she’ll be the determining vote on the legislation to repeal medevac, the law that facilitates medical transfers from Papua New Guinea and Nauru.

Lambie, everyone says, is “keeping her cards close to her chest”.

Meanwhile, behind the scenes a race is on to get as many people as possible with medical needs to Australia ahead of the vote, in case the government wins Lambie’s support.

A Senate inquiry on the repeal legislation is due to report on October 18. The government could try to push through its bill in the week of November 11, the next available Senate sitting week.

Those pursuing transfers on behalf of applicants claim the government is attempting to “run down the clock”, dragging out the transfers where it can.

Read more: Peter Dutton is whipping up fear on the medevac law, but it defies logic and compassion

The number of people offshore is now relatively small, after 632 have departed to the United States (with another 263 going through the approval process) and more than 1000 transfers, including accompany family members, to Australia over the years (these mostly not under the new legislation).

According to government figures as of Thursday, there are 281 people in Papua New Guinea (including refugees, non-refugees and some that are still being processed) and 279 in Nauru.

In relation to medevac, the government says there have been 283 notifications for medical transfer, with 127 transferred, 23 in the process of transfer and “numerous others” engaged at various levels. It says the minister has refused 54 cases for transfer and the Independent Health Advisory Panel (IHAP) agreed with the refusal.

The Asylum Seeker Resource Centre (which is a member of the Medical Evacuation Response Group set up to manage transfer requests under the medevac law), operating on slightly different figures - its numbers were as of September 29 - says the minister had given approval in 133 cases, while in 15 cases, the minister had been overridden by the IHAP. Refusals had numbered 39, ASRC says.

It says some 79% of all medevac applications that had been determined won approval. In 71% of cases decided, the minister approved the application in the first instance.

The medevac legislation passed when the Coalition was in minority at the end of the last parliamentary term. The government at the time warned of dire consequences, including that rapists and paedophiles would get to Australia.

It re-opened Christmas Island and said transferees would be sent there. No one has been. (Only the Tamil family is there. That family has lived in Australia for years but has failed in its bids for refugee status and will be deported if it loses its current court case.)

The government insisted medevac would trigger a reopening of the people smuggling trade. That hasn’t happened, and the several boats (not a flotilla) that have set out in recent months have been intercepted by the efficient turnback operation. Any “pull” factor is also offset by the medevac law only applying to people who came before it passed.

Read more: Lambie's vote key if government wants to have medevac repealed

Is medevac a way of clearing everyone from PNG and Nauru by the backdoor? No and yes. Not directly, because people have to be demonstrably ill. But after so many years, most of these people are or will be sick, mainly though not entirely with mental illnesses. Which of us would not be, in their circumstances?

Given there is not evidence medevac has compromised border security since its passage early this year, the government’s quest to repeal the legislation seems driven by anger (that it was imposed on it by Labor and the crossbench), ideology and politics.

If it were looking at the matter strictly logically, surely it would reason that the remaining people offshore present, in policy terms, what the political scientists call a “wicked problem” which medevac is helping solve.

These people can’t stay where they are for ever (and should not have been there anything like this long). More have been transferred to Australia than are now offshore. People who’ve been brought here under medevac remain in detention facilities (various places can be designated a detention facility) at the discretion of the minister.

If the medevac law helps end the offshore issue, isn’t this an upside for Australia without a demonstrable downside? That’s just putting things in crude policy cost-benefit terms. Behind this, of course, lies the compelling humanitarian case.

Read more: Explainer: how will the 'medevac' bill actually affect ill asylum seekers?

In the end, everyone waits on Lambie. The government is in her ear. So are those wanting medevac preserved. Her office says she is still taking “soundings”, although there has been a long time to get across the arguments, which aren’t particularly complicated. The Senate inquiry, chaired by the government, can be expected to come down on party lines, rather than adding much new.

Gross horse trading is now a feature of dealing with legislation in the Senate. While sometimes the Senate acts as a genuine house of review, at others it seems the proportional representation voting system, which has delivered so much clout to crossbenchers representing relatively few voters, has a lot to answer for.

No doubt the government would be willing to put a feast on Lambie’s table to get a win on what has become this totemic issue for it.

But this is a piece of legislation on which Lambie should not contemplate any deals, whether in response to carrots for Tasmania or anything else the government might hold out or she might want.

The key crossbencher’s decision should involve only judgements about morality, the medical needs and future lives of vulnerable people, and border security. On those criteria how she should vote seems pretty clear, even while she keeps everyone guessing how she will vote.

*This article has been changed to correct the Senate sitting date.