The Tánaiste Joan Burton is under pressure from Labour TDs to block the sale of Aer Lingus.
Party backbenchers are reported to be holding an emergency meeting today to discuss the €1.4bn takeover offer from British Airways owner IAG.
A number of TDs have voiced concern about the proposed deal over fears that jobs could be put in jeopardy.
The Taoiseach yesterday told the Dáil no decision has been taken on International Airlines Group's takeover bid for Aer Lingus.
However, many Labour TDs are opposing the offer, fearing for the party's prospects on Dublin's northside where most of Aer Lingus's Irish workforce are based.
Speaking to the Irish Independent, former Junior Minister Joe Costello warned the Government not to accept a "pig-in-the-poke deal".
In addition, Senator Lorraine Higgins called for IAG chief Willie Walsh to step down as non-executive chairman of the NTMA, saying she believes his advice on state assets represents a "conflict of interest".
Transport Minister Paschal Donohoe has asked a review group to advise him about the €1.4bn bid.
Earlier this week, the Minister labelled a planned protest outside his home by Aer Lingus pensioners "unacceptable".
Meanwhile, Fianna Fáil's finance spokesman Michael McGrath said selling Aer Lingus could have a "devastating impact" on the economy.
"They are exposing the country, and particularly the regions, to very significant risk," he said. "If there was any suggestion that those vital Heathrow slots could be lost for Cork Airport, for example, it would have a devastating impact on the economy.
"It's a risk we simply cannot afford to take."