Opposition assistant defence spokesman Phil Thompson has tendered his resignation after Mr Taylor stepped down from the shadow ministry on Wednesday night.
Mr Thompson and deputy whip Jess Collins have written a letter to Ms Ley, asking for an urgent party room meeting to resolve ongoing leadership speculation.
"We have been in a death spiral, and we need to get out of it. Angus Taylor has the ability to do that," Mr Thompson told reporters in Canberra on Thursday morning.
Mr Thompson said the timing of the spill would be up to the whip, who is responsible for organising meetings and MPs' movements.
Liberal senator Claire Chandler, previously the opposition's cybersecurity and science spokeswoman, has also announced her resignation from the shadow ministry and declared her support for Mr Taylor.
More resignations are expected throughout the day.
Ms Ley's backers concede any leadership vote will be tight, while Mr Taylor's camp insist they have the numbers.
Supporters of the current opposition leader argue she hasn't been given enough time to improve the party's position.
Backbench senator Sarah Henderson declared her support for Mr Taylor and backed moderate Jane Hume to run as his deputy.
"We cannot continue as we are. We've declined very rapidly since the election," Senator Henderson told reporters in the corridors of parliament.
Senator Hume, who was dumped from the shadow ministry after the 2025 election, said Mr Taylor would be a "terrific leader".
"He is a very deep thinker and a great intellect in our party. He's got incredible experience at a number of portfolios," she told Sydney radio 2GB.
"He's very good in city seats, but he comes from a country seat himself and is naturally a country boy.
"He's a very human human."
The former shadow finance minister also said her party was struggling in the polls and needed a change.
"No one is voting for us. No one is listening to us," Senator Hume said.
Announcing his resignation on Wednesday night, Mr Taylor said he had supported Ms Ley's leadership through a difficult period but it was time for change.
"We can't mince with words. The Liberal Party is at the worst position it has been since 1944 when the party was formed," he told reporters.
Mr Taylor's resignation has allowed him to openly canvass for votes before a leadership ballot.
"I don't believe Sussan Ley is in a position to be able to lead the party as it needs to be led from here," Mr Taylor said.
"What we need right now is strong leadership, clear direction and a courageous focus on our values, and the first two priorities should be protecting our way of life and restoring our standard of living."
Shadow attorney-general Andrew Wallace and housing spokesman Andrew Bragg said they still backed Ms Ley and she hadn't been given a reasonable opportunity to succeed.
Some of Ms Ley's backers have previously suggested a petition signed by a majority of Liberals must be presented for a party room meeting to be held - a similar tactic pulled by former Liberal prime minister Malcolm Turnbull when his leadership came under threat in 2018.
AAP understands Ms Ley is not wedded to that strategy and may be open to holding a meeting if just two MPs call for it.
20°C