Yesterday the Attorney General asked the Crown Prosecution Service (CPS) to pass on details about the case.
A decision will then be made on whether to send the case to the Court of Appeal for a sentence review.
The couple could be jailed for a maximum of 10 years.
Nicola, from Wolstanton, Staffs., said: "People here are absolutely disgusted with the sentence and they both deserve to be jailed.
"The sentence is unbelievable. It's like the judge is sending out a message to say that it's OK to be cruel to children.
"Drink-drivers get sent straight down, but these two have been allowed to walk free. I'm glad the Attorney General has listened to the protests and I hope it leads to them being given a proper sentence - in prison."
Stoke-on-Trent Crown Court heard X-rays revealed the child had suffered a catalogue of fractures to both arms, both legs, the left foot and left shoulder.
The child was also shaken by Gleaves, while a second child was slapped by Cartwright.
The couple were spared jail after Recorder Simon Ward heard it was their first offence.
He slapped them each with a 36 week prison sentence suspended sentences of two years.
Gleaves was ordered to complete 100 hours of unpaid work.
Recorder Ward told them: "You've both been convicted of very serious offences and you're going to have to live with the consequences.
"Offences of cruelty and ill-treatment of children are so serious that the courts have to send out a message to people that, if convicted, serious sentences will follow."
Cartwright and Gleaves, who lived in Wolstanton, have now fled the area.
A spokesman for the Attorney General's Office said: "We have asked the CPS for more information to decide whether the sentence should be referred to the Court of Appeal for review.
"The power to refer sentences is subject to a strict 28-day time limit from the day of sentencing.
"This case is within that time limit and either the attorney or the solicitor general will make their decision in due course."
The maximum jail sentence for cruelty to a child is 10 years.
At the lower end of the scale, the guidelines state a sentence of anything between 12 weeks in custody to a community order can be imposed for offences involving short-term neglect or ill-treatment, a single incident of short-term abandonment or a failure to protect a child.