Some 36% believe the main opposition party could make serious headway on the housing crisis, if successful at the next election.
According to the latest Red C/Sunday Business Post poll, just over a third of voters have confidence in Sinn Féin to resolve the housing crisis.
Some 46% believe that Sinn Féin could not solve the crisis at all, while 17% are unsure.
Elsewhere, the poll shows that 42% of people believe Sinn Féin could do a better job at improving health services that the current Government.
However, 45% of Irish people think foreign direct investment would reduce if Sinn Féin were elected.
A further 43% said they would not trust a Sinn Féin justice minister to tackle 'gangland crime and subversive activity'. Some 41% said they would trust a Sinn Féin minister.
Deputy McDonald previously said she would not have allowed convicted criminal Jonathan Dowdall to be a Sinn Féin member had she known he was involved in crime - 45% of people polled believed her. Some 37% did not believe Deputy McDonald's statement, while 19% remain unsure.
Leading parties
Despite this finding, Sinn Féin remains the most popular party in Ireland at 31%.
Fine Gael is also unchanged at 22%, while Fianna Fáil is up one, to 16%
The Green Party is up one point to 4%, while the Social Democrats are down one point to 5%.
Approximately 46% of Irish people polled believe opposition leader Mary Lou McDonald would make a good Taoiseach. A further 38% disagreed with this, while 16% were unsure.
The poll has also puts Tánaiste and Foreign Affairs Minister Micheál Martin as the highest-performing minister at 28 per cent - with his Fianna Fáil colleague in the Department of Housing, Darragh O'Brien, the lowest-ranking at 4 per cent.