Karen Webb has been accused of taking too long to front the public after the officer was charged on Friday, deflecting media scrutiny to her deputy and using flippant language to describe the crimes.
NSW upper house MP and former police officer Rod Roberts called on Ms Webb to be a "strong leader" and accused the senior officer of losing the support of her colleagues.
"There's absolutely no confidence from the troops at all ... from the senior management right down to those at the coalface," he told Sydney radio 2GB on Tuesday.
"She's not a leader, she's not leading them like a leader should do."
But Ms Webb defended her right to stay in the top job, using a Taylor Swift song lyric to fend off the criticism during a media blitz on Tuesday morning.
"There will always be haters," she told Seven's Sunrise program.
"Haters like to hate ... isn't that what Taylor says?"
"I have a job to do ... it is a big job (and) this is just one of many.
"We actually had seven murders last week."
Ms Webb also came under fire for her choice of wording about the alleged murders, which she described as a "crime of passion" during her first press conference about the case on Monday.
"What I did say was it is a crime and of course (it is) domestic violence, stalking and murder," she told Nine's Today program on Tuesday.
"What I was intending is to say that it's actually not a gay hate crime."
Senior Constable Beau Lamarre-Condon has been accused of murdering Luke Davies and his boyfriend Jesse Baird after an alleged months-long campaign of "predatory behaviour" against Mr Baird, whom he had briefly dated.
Constable Beau Lamarre-Condon was charged with two counts of murder on Friday. (James Gourley/AAP PHOTOS)
Ms Webb's deputy David Hudson took control over much of the media scrutiny on Monday, speaking for most of the press conference and overshadowing the commissioner.
But on Tuesday Ms Webb said the benefit of being a leader was that she had "a good team" around her.
She also conceded that "something went wrong" with police firearm procedures in allowing Lamarre-Condon to have access to his official weapon, which was allegedly used in the murders.
"This will cause another review and rightfully so," she said.
Ms Webb said the investigation would also work through other issues surrounding Lamarre-Condon's employment with NSW Police, including his recruitment and assessments "to see if there are any red flags".
Mr Roberts earlier criticised the decision to recruit Lamarre-Condon, a former celebrity blogger, while also attacking Ms Webb for her handling of media scrutiny over her approach to the case.
"They were fair questions that were put to her and she just went into attack mode," he said.
When asked on Tuesday if she was up to the job, Ms Webb replied: "Of course I am."
