The leadership meeting will take place at 9am on Friday in Canberra.
Mr Taylor, a senior conservative from NSW, argues dire polling means Sussan Ley is no longer the best person to lead the opposition and he is the man for the job.
James Paterson and Jonno Duniam are the highest-profile resignations, both having sat alongside Mr Taylor on Ms Ley's small leadership committee.
Senator Paterson said Ms Ley's leadership was untenable as the Liberals tanked to historic lows in numerous polls and were overtaken by right-wing minor party One Nation.
The polls, putting the coalition's primary vote as low as 18 per cent, meant the party had lost millions of supporters since the May election, the former finance spokesman said.
"This cannot go on. If it goes on, there will be nothing left of the Liberal Party at the next election," Senator Paterson told reporters on Thursday after tendering his resignation.
Senator Duniam said internal party bickering needed to end so the opposition team could unite and focus on holding the Labor government to account.
"Sussan has worked harder than many will ever know and I have stood with her all the way, but this matter must now be resolved and our party needs to get on with the job of winning back the trust of Australians," he said.
Both senators accepted some personal responsibility for the Liberals' polling plunge.
A leadership ballot will take place during a special partyroom meeting at 9am Friday, two Liberal sources told AAP.
The opposition leader has maintained her silence on the resignations and Mr Taylor's challenge, only putting out a social media post outlining a plan for "a better future" by taking the pressure off families, fixing the budget and keeping Australians safe.
Shadow attorney-general Andrew Wallace and housing spokesman Andrew Bragg said they still backed Ms Ley, with the latter saying she should have been given at least a year in the job.
Senator Paterson denied rolling the Liberals' first female leader so early in her tenure exacerbated the party's problem with women's representation, saying leaders were judged on performance and Ms Ley had the worst approval rating for an opposition leader in decades.
"It is clear what the verdict on her leadership is," he said after pointing to Labor knifing the first female prime minister, Julia Gillard.
Conservative Liberals Phil Thompson and Jess Collins officially petitioned Ms Ley on Thursday morning to call a party-room meeting to decide the leadership.
Mr Thompson and other shadow ministers, including Matt O'Sullivan and Claire Chandler, then tendered their resignations from the front bench to support Mr Taylor.
While most expect the vote to be tight, coming down to one or two ballots, one MP - who isn't counting votes for either party - said conversations with colleagues revealed Ms Ley's time as leader was over.
Mr Taylor was poised to win with somewhere between five and 12 extra votes, they said.
Ms Ley initially beat Mr Taylor in a leadership contest 29 to 25 after the federal election, but three of her supporters have since left the party room.
One Ley supporter said anyone predicting an overwhelming win wasn't well-informed.
Ms Ley is weighing up the pros and cons of calling the meeting immediately and waiting an extra day.
She is balancing the need to strip Mr Taylor of momentum against letting him and deputy leader aspirant Jane Hume face further scrutiny over failings during the last election campaign, supporters say.
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