Within 24 hours the petition for the Attorney General to review Roger Goodall's sentence has gained thousands of signatures from people all over the country.
In September, the 77-year-old of The Mount, Shrewsbury, was jailed for four-and-a-half years for causing the death of Olivia-Violet Reeves, from Worthen.
The youngster was killed when Goodall’s out-of-control car hit her as she walked to catch the bus home from school in Shrewsbury.
Last week, Olivia-Violet’s family applied to the Solicitor General for permission to appeal the sentence, which they said was too lenient, but just a few days later they learned that they had been unsuccessful.
Olivia-Violet's uncle, Simon Reeves, said he hopes that the petition will gain 100,000 signatures so the family can present it to parliament.
He said: "I was hoping it was going to go UK-wide, and people have started signing it from all over the country now.
"The petition was launched by a friend of Olivia-Violet's mum.
"It's brilliant, hopefully it will keep going, we want the full 100,000 signatures. We want to go to Downing Street and it can be put forward for debate in parliament."
He added: "People are supporting it because it's a complete injustice. There's no justification for the way he was sentenced, there was no remorse at all.
"The only justification is the guilty plea but he pleaded guilty at the last minute.
"There was an opportunity for him in court to have a statement read out to say how sorry he was, he could have done numerous things but he chose to do nothing."
Mr Reeves said Goodall should have been given a 'level one' sentence, not a reduced 'level two' sentence for personal reasons.
"He should have been sentenced on a level one and not a level two and that way he would have got eight years," he said.
"You look at the court system and the judiciary system, we're going to have to go to court just to get permission to appeal before we can appeal anyway.
"Look how long it took Hillsborough, it was years and years.
"It's comforting in a way to know its not just us being stupid or nasty or vindictive, there's a lot of people who are feeling the same way and are behind us.
"It makes me feel like we're doing the right thing. It's been signed and shared by so many people now that it seems like it's unstoppable."
People have been signing the petition in Shropshire but also areas such as Milford Haven in Wales, and Widnes.