People Before Profit TD Joan Collins called on people not to register for the household charge in the New Year.
The group is also calling on the Government to scrap proposals for a property tax.
It rejected suggestions this was a PR stunt by TDs and said they were being contacted by constituents who said they could not afford to pay.
Minister for the Environment Phil Hogan has said that any property tax would be fair but the national body for residents' associations, ACRA, said it was not a tax on property but rather a tax on peoples' homes.
Independent TD Thomas Pringle described Minister Hogan's property tax proposals for as early as 2013 as a "complete reaction to opposition".
He said opposition to the household charge was "palpable" among constituents and urged more protests so the Government "can see and hear the anger of the people that elected them".
The Taoiseach has said he wants the property tax to be affordable, equitable and ultimately the responsibility of the country's local authorities.
Enda Kenny said details of the measure would have to await the report of an expert group, but he expected it to raise €500m annually.