Green TDs Nessa Hourigan and Patrick Costello have told their party's leadership that they will not back the Government in a Dáil vote this week.
A short debate followed by a vote on the Comprehensive Economic Trade Agreement (CETA) was scheduled to take place in the Dáil tomorrow.
CETA is a trade agreement reached between the EU and Canada which requires the backing of parliaments across all the EU Member States to be fully operational.
So far it has been endorsed by 14 national parliaments.
While the agreement got the backing of Cabinet two weeks ago it has run into difficulty ahead of a planned vote.
The two Green TDs say they can not vote for it with Ms Hourigan insisting her party had negotiated to keep CETA out of the programme for Government.
However, Government sources point out this programme does commit to endorsing EU agreements.
The matter will be discussed by the Government party leaders later but it is likely the vote will be postponed.
People Before Profit TD Richard Boyd Barrett described the Government motion as a sleight of hand at the end of the Dáil term.
He said this was aimed at pushing through a trade deal that has profound implications for the required actions to tackle the climate crisis.
This view is shared by Sinn Féin and the Social Democrats.
Sinn Féin's agriculture spokesperson has accused the Government of attempting to use the crunch Brexit negotiations as cover to "sneak through" a vote on CETA.
Matt Carthy said there was a need for a comprehensive analysis of the implications of the deal before any ratification vote is brought before the Oireachtas.
CETA was a trade deal struck between the EU and Canada in 2017.
It has been operating on a provisional basis since then and has cut tariffs and red tape as €72.3 billion were traded in goods between the EU and Canada in 2018 alone.
However, to give full effect to the agreement all national parliaments in the EU must vote to give it the green light.
This was due to happen in the Dáil tomorrow, but the vote is almost certain to be postponed following unease within the Green Party and among the opposition parties.
Those opposed to CETA say it allows large corporations to sue countries if regulations hinder those companies' ability to trade.
Sinn Féin, the Social Democrats and Solidarity-PBP claim this would put in jeopardy future legislation aimed at protecting public services and tackling climate change.
