People Before Profit's Richard Boyd Barrett says it doesn't appear as if the left-wing parties in the Dáil have the numbers to form a left government.
With all 160 seats in the Dáil now filled, the focus has shifted to what form the next government could take.
Sinn Féin's Mary Lou McDonald is beginning discussions with parties such as the Greens and Social Democrats with the aim of forming a left-wing coalition.
However, there is no immediate or traditional path to a majority government for Sinn Féin, Fine Gael or Fianna Fáil.
Sinn Féin + Greens + Labour + Soc Dems would be 61 seats. If they could come together as a left block, could they convince FF into a left-led coalition or C&S? Stronger influence on prog for govt together. Still seems far-fetched, but what isn't at this stage #GE2020
— Seán Defoe (@SeanDefoe) February 10, 2020
Solidarity - People Before Profit TD Richard Boyd Barrett told Newstalk Breakfast his group - which returned five TDs to the Dáil - will be meeting with other parties in the coming days
He observed: "There has been something of an earthquake in terms of Fianna Fáil and Fine Gael now having considerably less than 50% popular support.
"It's a poor result for the establishment, and we're glad that many people have made that move.
"But if you look at the numbers - much as we campaigned for and suggested that a left government was possible - I think probably we haven't got the numbers.
"I think there will be discussions among parties of the left over the next week about what can be done, but it would appear we don't quite have the numbers".
He stressed that he is "very enthusiastic" about voters' demand for change - but suggested that the 'raw numbers' in the Dáil are not necessarily on their side.
On possible governments, Deputy Boyd Barrett said: "I would imagine there will be discussions between Fianna Fáil and Fine Gael about the possibility of forming a government... Sinn Féin and Fianna Fáil and possibly the Greens might have the numbers for a government.
"I think the priority for us is how do we keep the momentum to the left going, and look at how could the left build an alliance - if we haven't quite got the numbers for a left government this time around, it's tantalisingly close."