The by-election for the wealthy seaside constituency of Wentworth, in Sydney's east, followed the resignation of former prime minister Malcolm Turnbull who was ousted in August by his own party.
As the count from a crucial Australian by-election spilled into Sunday, Prime Minister Scott Morrison faced the possibility that his Liberal party may have been too quick to concede a contest that would relegate his administration to a minority government.
But she has all but ruled out helping force an early election or supporting a no-confidence motion in the government.
Her lead stood at just under 900 votes on Sunday, and it must drop to below 100 to automatically trigger a recount.
"This is over tonight a little sooner than I expected, and I am certainly glad I kept my day job", he joked. The opposition Labor Party holds 69 seats, while independents have six.
An election poster of Liberal candidate Dave Sharma is seen on a street in the seat of Wentworth in Sydney on October 18, 2018.
The by-election was sparked by the resignation of Turnbull from parliament after he was dumped as Liberal party leader and prime minister.
Should the Liberals lose Wentworth, Morrison's conservative coalition will probably have to rely on support from independent lawmakers to survive the next few months, as a general election is due by May next year.
She argues the outcome may not even be known on Saturday night.More news: Donald Trump threatens to CLOSE border with Mexico - ‘Stop this onslaught!’
Morrison said that while the loss was not unexpected given opinion polls, his party had received a loud message from voters.
It is understood that Mr Sharma is not interested in a Senate seat, and the only one available to him would be the spot promised to Andrew Bragg, who pulled out of the preselection race because he felt a female candidate was the Liberal's best hope in Wentworth.
"We will work constructively with all of those who sit on the cross bench as we always have", he said.
"What we have done is tapped into a sentiment in the Australian people, to talk about the issues that are important to them, not the issues about survival for a particular political party", Phelps told supporters during her victory speech.
Meanwhile, Treasurer Josh Frydenberg says the government will continue to seek assurances from crossbenchers to hold off the threat of an early election.
The by-election campaign, in a seat with a large Jewish population, drew global attention this past week when Morrison raised the prospect of following the United States by relocating Australia's embassy in Israel from Tel Aviv to Jerusalem.
But by Sunday evening, his candidate trailed an independent rival by 1,600 votes with several thousand votes still to be counted, the Australian Electoral Commission (AEC) said.
Israeli Prime Minister Benjamin Netanyahu had welcomed Morrison's announcement, saying in a statement on Tuesday that he was "very thankful" the prime minister was considering the policy change.