The Hobart-based senator is third on the Liberals' state ticket and is not guaranteed an ongoing place on the upper house benches, where he has sat since 1994.
Voting in suburban Hobart on Saturday, the 64-year-old continued to campaign for a coalition government, in the knowledge it could be several days before he knows his own political future.
"The support I've had has been very heartening," Senator Abetz told News Corp.
"(I'm) always nervous on election day and it's up to the people to decide," he told ABC Radio.
Senate colleagues Jonno Duniam and Wendy Askew won first and second place respectively on the Tasmanian Liberal ticket.
In the north of the state, the electorate of Bass is the nation's most marginal Liberal seat.
Former George Town mayor Bridget Archer is defending her 0.4 per cent margin, fighting off a resurgent Ross Hart who she took the seat from in 2019.
"Whatever happens, I am really proud of what I've achieved in Bass," she told News Corp on Saturday.
"I've tried to work hard for the community and connect with them throughout my term. It's not good enough to just turn up at campaign time."
On Friday, Ms Archer denied distancing herself from the Liberal Party in the countdown to the poll.
Advertising for Ms Archer in recent days has not included the Liberal logo and has featured the colour purple, rather than the usual blue used for the party.
"My volunteers are covered in Liberal branding ... I'm a proud member of the Liberal Party, I remain a proud member of the Liberal Party," she told reporters in Launceston on Friday.
"The fact that people are talking about the purple signs probably means they are doing their job."
Hobart Independent MP Andrew Wilkie remained in isolation with COVID-19 on Saturday, but his position is not considered to be at risk, holding the seat of Clark with a 22 per cent margin.
He plans to join his election night function via video call.
Across the Derwent River in the seat of Franklin, long-term Labor MP Julie Collins is expected to become a minister in an Anthony Albanese government.
"I'm hoping for a good result," she told News Corp on Saturday.
"I've felt it was a pretty positive campaign on the ground and people want to get rid of Scott Morrison."
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