Deputy Dakota Palanca was responding to a call of a person acting erratically in Paramount on Nov. 25 when she was struck by an SUV, investigators said.
Palanca's mother is grateful for the outpouring of support her daughter has received.
"I know what I have in my heart and what I see in my child and she's just going to keep fighting and get better and better," said Lori Hayden, Palanca's mother.
The 25-year-old's stepfather said that Palanca comes from a law enforcement family and that his daughter is trained to do the job both locally and with the military.
"She has always wanted to defend the country and the community and the nature of the business is uncertainty and very dangerous at times, but she was made for this. She was doing what she loves to do," said Rick Hayden, Palanca's stepfather.
Funds raised at a barbecue and donations to the deputy's union will help with Palanca's immediate costs.
All funds that go to the Association for Los Angeles Deputy Sheriffs through Jan. 11 will go to Palanca's family, said Ron Hernandez, president of ALADS.
L.A. County Sheriff Alex Villanueva said his department will give Deputy Palanca what she needs to get her through the traumatic brain injury she suffered in the line of duty.
"We'll remain there until we get her out of critical condition...we get her stabilized and in the long process of occupational therapy...to get her back on her feet and, Lord willing, get her back to work one day," Villanueva said.
Palanca's mother said she knows that her daughter is fighting.
"When I walked in yesterday, she showed off and opened her eyes for me...I'm going 'Overachiever, this kid is just an overachiever," Lori said.
Palanca was expected to undergo a cat scan Thursday to determine whether it is safe for doctors to remove a stent from her head that was relieving pressure from her brain.