"Doctors have told us to be prepared for any eventuality," his wife, Gemma, told The Manchester Evening News.
"I just need him to pull through. Gaz is the kindest, nicest man ever, he keeps himself to himself, he's so chilled out. He'd never hurt anyone or say anything bad about anyone. I just can't believe this has happened, it's like living in a nightmare.
"I can't imagine why anyone would do this."
She added: "It's been amazing, it's just so reassuring to know how loved and highly regarded he is.
"Everyone has been so supportive and it's just brilliant.
"There are hundreds of messages, I can't keep up - Twitter, Facebook, Whatsapp, phone calls, emails. It just shows everybody loves Gaz. We need him to get well."
Former Warrior and injured England fullback Sam Tomkins tweeted a message of support to Mrs Carter, saying: "He's a good guy who Iv always enjoyed working with. We're all supporting him. Let me know if there's anything i can do."
A 35-year-old man has been charged with grievous bodily harm and a 22-year-old man was arrested for affray and released on bail until late November.