After just five months in the Senate, Jacqui Lambie is already one of most-recognisable federal politicians in Tasmania, perhaps only behind Eric Abetz, the Minister for Employment.

For most politicians, that level of prominence would be gold dust. But as everyone who follows Australian politics knows, the former army corporal isn't a regular politician.

Lambie's sudden prominence has left Tasmanians with sharply polarised views. Some see her as a rough but brave woman who expresses the views of ordinary voters. Other think she's dangerous, unbalanced and an embarrassment to Tasmania.

"Do a vox pop in the middle of Hobart almost everyone will say she is crazy or something like that," said Kevin Bonham, a Tasmanian polling analyst. "You go to the north of the state and the reaction could be quite different."

Lambie grew up in the north-western Tasmanian city of Devonport, attended the local high school and spent 10 years in the army. She has two sons and a long-running workers' compensation dispute with the Department of Veterans' Affairs. She ended her maiden speech on a patriotic note: "God bless my Tasmania and our beautiful Southern Cross."

Lambie's background endears her to many people in Tasmania, where at least one third of adults receive some form of welfare, 10 per cent are considered "working poor" and many others rely on government jobs.

If Lambie decides to the leave the Palmer United Party - and she was considering her future over the weekend - it is unclear if she has enough personal support to be re-elected as an independent.

Kate Crowley, a political scientist at the University of Tasmania, believes Lambie's determination to put the state before her party would deliver her a second term if she could raise enough campaign funds.

"Tasmanians prefer their senators to represent the state and not parties," Crowley said.

"It's extraordinary how many people in Tasmania like her, despite who she is and how she comes across and the fact she is telling the Prime Minister to toughen up and calling him a psychopath and a barefaced liar. Most people in Tasmania are saying good on her."

Steve Martin, the mayor of Devonport, saw her at a local awards presentation a month ago. He says he gave her some advice: develop her own political style as she learns how parliament works.

"I think the media is being a bit hard on her," he said. "She is courageous and that's a good thing."