Another grim Newspoll for the opposition saw the party's primary vote hold at the record low of 24 per cent, while Labor lifted its lead to 16 points after preferences.
Conservative senator Sarah Henderson, who previously said Ms Ley was losing support in the party room, warned the opposition had a "very big mountain to climb" if it wanted to return to government.
"We've got a lot of work to do to win back the trust and faith of all Australians," she told Sky News.
Pressed on whether she would move a spill motion against Ms Ley in Tuesday's partyroom meeting, Senator Henderson said she had no plans for the week "other than to prosecute really good policy".
Conservatives have indicated while the poor Newspoll showing would put pressure on Ms Ley's leadership, a challenge wasn't expected until next year.
Despite doing dozens of media interviews making the case for the opposition's plan to scrap Australia's climate targets and prioritise lower power bills, Ms Ley only slightly improved her approval rating, from negative 33 to negative 29.
The survey showed Ms Ley, a moderate, was nominated by just 21 per cent of voters as their preferred leader of the coalition, including 28 per cent of coalition voters.Â
Ex-SAS soldier Andrew Hastie was second overall, with backing from 15 per cent of voters, and the first choice of elderly Australians and One Nation voters.
Angus Taylor (nine per cent), Tim Wilson (six per cent) and Ted O'Brien (three per cent) also received support from voters.
Ms Ley's allies were keen to point out women and young people were significantly more likely to support her than other leadership contenders.
Barnaby Joyce, who is yet to finalise a months-long flirtation with anti-immigration party One Nation, said voters were frustrated with the coalition.
"Out of frustration, they've gone shopping. Political shopping," he told reporters in Canberra on Monday.
Mr Joyce said he wouldn't announce his next political move, which is widely expected to be a defection to Pauline Hanson's party, until at least the end of the week.
"I just don't want any circus ... if I was doing anything I'd try and get out of the building (first)," he said.
The opposition used question time on Monday to press the government on the decision to appoint Chris Bowen to president of negotiations for next year's UN climate conference, while also serving as federal energy minister.
Coalition MPs attacked Mr Bowen as a "part-time" energy minister who has presided over higher power prices, but Treasurer Jim Chalmers fired back.
"They couldn't give a toss about electricity prices for Australia," he said.
"All they care about is the internal politics is of the inner coalition rooms and this is what we see with this unedifying behaviour."
