A Sinn Féin motion that would ban rent increases for three years is being debated in the Dáil.
The party's housing spokesperson Eoin Ó Broin said it signals "a radical change of direction", and includes a rent rebate that would put at least a month's rent back in peoples' pockets.
The bill also commits to faster delivery of affordable homes.
It would introduce "real tenancies of indefinite duration, and not the smoke and mirrors change that you introduced last year," he said to Housing Minister Darragh O'Brien.
"Renters can't take any more", Deputy Ó Broin said.
Sinn Féin TD Louise O'Reilly said that she is dealing with people facing eviction in each clinic she holds.
Most recently she spoke with a couple in their seventies, and a woman in her sixties who is "sleeping in her car".
The indignity of this "after a lifetime of work" is appalling, she said.
"The housing crisis in Cork has never been as bad as it is now", party colleague Thomas Gould said.
He is dealing with twenty families who are facing eviction.
"They are desperate, and they have nowhere to go", he said, adding that the bill before the House is part of the solution.
Minister O'Brien said that Sinn Féin has supported ten of the eleven pieces of legislation he has tabled over the past 12 or 14 months - and yet noted that they say that he is doing nothing right.
In bad-tempered exchanges, Mr Ó Broin interrupted the minister and the two men spoke over each other, with the minister saying he "won't be bullied or shouted down".
The Ceann Comhairle warned that he would suspend the House if the behavior continued.
Looking at the Sinn Féin benches, Sean Ó Fearghaíl condemned "strategic heckling", and warned action would be taken to "put a stop to it" if it continued, as it is "objectionable".
Everyone has the right to make their contribution, he said, and that includes the minister.
Labour's Seán Sherlock said that the debate has become "quite personalised".
He added that this does not help those on the housing list.
Cian O'Callaghan, Social Democrats, noted the "22% increase in homelessness in the past year", and a "30% increase" in the number of children who are without a home.
Both Deputy O'Callaghan and Louise O'Reilly criticised Minister O'Brien for his remarks over the weekend linking economic migrants to the rise in homelessness.