Stephen Termini (57), from New York state, was seriously injured in an attack on Talbot Street in the city centre on July 19.
The incident has prompted a wider debate on whether Dublin’s streets are safe.
On Friday, Minister for Justice Helen McEntee announced an additional €10 million for Gardaí in the Dublin region.
Mr Termini’s sons, Michael and Jesse Rizzuto, have travelled from the US to visit their father in hospital.
They set up an online fundraising page with a target of $10,000 (€9,000) to pay for their trip to Ireland.
The Go Fund Me page has been deluged with donations. By Saturday the total raised had passed $127,000 (€115,000) with more than 4,400 people having donated.
Jesse Rizzuto said the reaction had been “nothing but the greatest”.
“Everybody has reached out to us to say ‘You know, this isn’t what it’s like (in Ireland), we want to show you what it’s like’,” he told RTÉ.
“And I mean the donations, we never expected a turnout like this.
“I mean we had it set for a smaller amount just to get us over here and see him, but I mean everybody that’s donated has left us comments as well like ‘hey, you know, so sorry’ or ‘hey, all the best for your family, this isn’t what Ireland’s really like and the people don’t stand behind that’.
“And it’s amazing.”
He added: “How do you thank over 4,000 people?”
His brother Michael added: “We’re just so thankful about everything. Like I wish I could just line everyone up and shake everyone’s hand and give hugs and stuff.”
Michael Rizzuto said his father was out of a coma, but improvements in his condition were slow.
“It’s going to be like a long game here,” he said.
Jesse Rizzuto said there were signs of “slight improvements” in his father’s condition. “We’re taking it basically one hour at a time,” he said.
“But he is making slight improvements that we’re very happy with, very happy with, he’s showing some good signs of having a strong resilient body.”
Asked about the extent of an injury to one of his father’s eyes, Jesse Rizzuto added: “They’re still trying to do everything they can.
“So we’re leaving it up to their hands because they’re the professionals. Yes, as far as injuries go, yes, he’s improving.”
Three teenage youths have appeared in court in Dublin charged in connection with the assault on Mr Termini.
David Young, PA
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