Minister for Finance Michael Noonan has said homeowners whose houses are affected by pyrite may not have to pay the Local Property Tax.
Opening the Dáil debate on the bill, Mr Noonan said that houses demonstrated to be subject to a certain level of pyrite damage could get a waiver.
He also told TDs that those who fail to pay the tax will be unable to get a tax clearance certificate.
Sinn Féin Finance Spokesperson Pearse Doherty said there would be no exemptions for homeowners in mortgage distress, in negative equity or those who paid stamp duty during the property boom.
Mr Doherty said nearly a quarter of all mortgages were in distress in 2012. He said next year would be even worse due to the effect of the Budget.
Fianna Fáil Finance Spokesperson Michael McGrath said the bill was being "rammed" through the Dáil.
Mr McGrath said there was no logical reason why the House could not consider it in its own time in January.
The bill was later passed in a Dáil vote.
Around 100 people gathered outside the gates of Leinster House to protest against the tax.