The group was set to meet twice on Tuesday
Fine Gael has abandoned a meeting of the Oireachtas Joint Committee on the Future Funding of Domestic Water Services, after losing in a series of votes earlier.
The party was defeated 14-6 in a vote to have the water system funded through general taxation.
The committee met at lunchtime Tuesday and was due to gather again later.
But the six members from Fine Gael have made themselves unavailable.
It is believed the party wants to take time to consider the votes which will be reflected in final report.
Meanwhile the Right2Water campaign has described the excessive usage charge as a 'trojan horse' to return to water charges.
The group has described the Water Committee report as a substantial victory for people power - but says there is a still a long way to go.
Thousands are expected to protest in Dublin this weekend calling for all water charges to be abolished and for metering to be scrapped.
Solidarity TD Paul Murphy said earlier: "It is currently an offence to waste water, it should continue to be an offence to waste water.
"And there should be a sanction for that and there should be a court process for that.
"The reason that the issue of a court process is important is because it means it can't become a back door for water charges - because it's a long process: they have to bring people to court, people have to collect evidence to say that they're not wasting water, etc.
"I think there's an important distinction and the report currently leaves that very, very open".
The committee is due to publish its final report on April 14th.