Some 58 TDs and more than 20 senators are backing a petition to President Michael D Higgins seeking a referendum on the water services bill.
Sinn Féin wants to petition the President not to sign the water services bill into law.
Senator David Cullinane says his party is seeking to petition President Higgins not to sign the bill - currently being debated in the Seanad - if it is passed in both Houses of the Oireachtas.
The President would be required to convene the Council of State to consider the bill under Article 27 of the Constitution if one third of the Dáil and a majority of senators sign a petition of concern after the bill has been passed by both Houses of the Oireachtas.
The bill was passed by the Dail on Thursday by 81 votes to 58. The legislation then moved to the Seanad, with the debate set to resume today.
Senator Gerard Craughwell has been gathering support over the weekend.
He says he has just about enough signatures to put to the President this week.
Meanwhile Tánaiste Joan Burton has lashed out at the protestors who trapped her in a car in Jobstown, comparing them to fascists.
Ms Burton says it is totally unacceptable to be trapped as she was for two hours.
The comments come as the water services bill goes before the Seanad for the final time.
Ms Burton says the protest was fundamentally anti-democratic.
Senator John Crown spoke with Jonathan Healy on Lunchtime today and stated that he would be voting against the bill, stating that the infrastructure should have been fixed first: