Former state and federal Liberal staffer Brad Stansfield, a partner at Font Public Relations, reported on his podcast a number of party members want to have Ms Archer replaced.
He said Ms Archer's decision to side with Labor on a number of votes in parliament and speaking out on a range of policies had made her a target in a party which claimed to be a "broad church".
"It's hardly a broad church when you seek to excommunicate someone whose views you disagree with," Mr Stansfield said on the podcast.
Liberal leader Peter Dutton told reporters on Wednesday the member for Bass worked hard and represented her community.
"Bridget Archer is an important part of our team," he said.
Mr Dutton said there was a "greater capability" in the Liberal party room, compared with Labor, for members to take a different view to colleagues.
"I hope that Bridget can continue to work with her colleagues in Canberra."
Ms Archer has backed part of Labor's climate plans and its housing legislation, and voted to censure former Liberal prime minister Scott Morrison over his secret ministries.
A list on the They Vote For You website shows she has cast her ballot contrary to the Liberals on 26 occasions since entering parliament in May 2019.
She also signalled she was open to a discussion on paring back superannuation tax concessions, which Labor is proposing.
The moderate Liberal holds the Launceston-based seat with a margin of 1.43 per cent.
The next federal election is due in early 2025.
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