The latest Red C opinion poll shows a drop in support for Fine Gael from 29% to 25%.
The poll, conducted for Paddy Power, suggests a backlash against the main party in Government over a range of issues such as property tax, water restrictions and controversy over health spending cuts, including medical cards.
The poll also shows overwhelming support for same-sex marriage.
However, the 4% drop in Fine Gael support is mirrored by a 4% increase in support for Independents, suggesting the drop could be short term.
The nationwide poll was conducted between 4 and 6 November.
Party support, compared to the last Red C poll in October, is: Fine Gael 25% (-4%), Labour 9% (no change), Fianna Fáil 24% (+1%), Sinn Féin 16% (-1%) and Independents and Others 26% (+4%).
Of those polled, 76% said they would support the referendum to allow same-sex marriage and 18% said they would not while 6% said they "don't know".
When the "don't knows" are excluded, the result is 81% support same-sex marriage.