The latest opinion poll published today shows that 40% of voters are opposed to the setting up of the National Assets Management Agency.
Over a quarter of voters are in favour of NAMA, while a substantial 34% have no opinion.
The strongest support for the government plan for removing bad loans from the banking system comes from the 25 to 34 age group.
In terms of social class, the strongest support at 32% comes from the wealthier sectors.
The poll also shows that Green party supporters are the most strongly opposed group.
It raises serious issues for the coalition partner - which is due to hold a special conference in Athlone next week to coincide with the NAMA legislation.