The idea of being Trump's running mate- and the despair one of his acolytes might feel about the sense she was likely not his first choice- is likely at the root of the bitter rivalry which has now developed between Greene and Lauren Boebert- Boebert is probably desperate to get the job, given that she nearly lost her House seat in November and very likely senses that she has no real future in Colorado GOP politics.
The desperation to be picked for the VP may also be what's driving Kari Lake's stubborn refusal to accept her defeat in the Arizona governor's race- she's out of a job, doesn't have any winnable offices to run for in that state, and likely sees carrying on an endless refusal to accept her defeat as the one way to get Trump's attention.