On the Sky News Electoral Dysfunction podcast, former Scottish Tory leader Ruth Davidson said Ms Badenoch is "running into trouble" and may only have 18 months in the job.
On Boxing Day, when Mr Farage claimed Reform UK had overtaken the Tories' 131,000 members, Ms Badenoch claimed the figures were fake.
In that speech, she criticised Theresa May and Boris Johnson for leaving the EU without a plan, Mrs May again for net zero targets without a plan and Mr Johnson and Rishi Sunak for promising to reduce immigration while it rose to record levels.
As well as bowing to pressure from critics in her party to announce some policies, it was seen as a response to Reform UK topping a Sky News/YouGov poll for the first time.
He has also annoyed her by repeatedly refusing to rule out a Tory pact with Mr Farage and Reform UK, something she has emphatically rejected.
