An Irish Times poll for Cork North Central shows that Socialist Party/United Left Alliance candidate Mick Barry may take the fourth seat with 13% of the first preference vote.
The alliance will be contesting for seats in areas across Cork and Dublin.
Along with Joe Higgins (Dublin West), Richard Boyd Barrett (Dun Laoghaire), Seamus Healy (South Tipperary) and Declan Bree (Sligo North Leitrim) they believe that Joan Collins (Dublin South Central), Clare Daly (Dublin North), Gino Kenny (Dublin Mid West) and Mick Murphy (Dublin South West) may also be elected.
If elected in sufficient numbers, the ULA said they will provide principled opposition to the agenda of austerity and cuts in the Dáil.
Councilor Barry said: "This poll confirms the feedback from our canvass. The people of Cork North Central want to see a real fighter in the Dail who will oppose the cuts agenda and ensure the voices of working people are heard.
"I urge my supporters not to be complacent. In the next 10 days we can expect ferocious attacks on the ULA. We must work until the last minute to ensure this historic opportunity is not lost."
Councilor Gino Kenny of the People Before Profit (Dublin Mid West) said: "This poll does not surprise me. The response on the doors has been great. People want real change and the ULA is the only force that can offer a radically new approach. Voters know we will campaign against the cuts and universal social change which has hammered the lower paid."
Mick Murphy of the Socialist Party, (Dublin South West) said: "This poll confirms that the ULA has truly arrived as a new force in Irish politics. Since its foundation in November it has gone from strength to strength.
"We are the only force that will offer genuine opposition to the agenda of the right wing parties. Voters are turning to us because they know a vote for Labour will not lead to a radical change but to a government dominated by the same failed policies of cuts and austerity."