In an interview with the Irish Independent, Mr Gilmore said this was not the time for Labour to "flinch" from its role in Government.
The Tanaiste also reiterated that the Coalition would make a decision next week on what action to take on abortion on foot of the recommendations in an expert group report.
"We will have decided the option this side of Christmas," he said.
Mr Gilmore came out fighting as he rejected suggestions Labour should pull out of Government.
"While there are people who may look for easier political options, now is not the time for this Government or for the Labour Party to flinch from the task that we undertook," he said.
After voting against the Government, Labour TD Colm Keaveney is refusing to give up his position as party chairman. Labour is going to remove the Galway East TD from three Dail committees following his expulsion from the parliamentary party for voting against the Budget social welfare cuts. The party is now expected to throw its resources behind Galway-based Labour Senator Lorraine Higgins, who has launched a strong attack on Mr Keaveney for "political grandstanding" and "the pursuit of self-interest".
But Mr Keaveney is insisting that he is entitled under the Labour constitution to stay on as party chairman until his term expires in April – and has told party figures who are criticising him to stop "playing the man and not the ball".
"I have just been overwhelmed by the fairness of members who describe any attempt to engage in anti-democratic conduct against the Labour chair of the party as profoundly anti-Labour," he said.
Mr Keaveney opted to return to his base in Tuam in Galway to be with his family and supporters rather than take part in the Dail debate on the property tax. He said he had got phone calls and emails from hundreds of Labour Party members, Labour Party councillors and constituents.
He also responded to the attack by Communications Minister Pat Rabbitte, who accused him yesterday of "self-indulgence" and "pirouetting on the plinth" in Leinster House rather than supporting hard decisions to get the country's finances back on track.
"We should focus on our decision here to break a promise made to the people on child benefit. His constituency (Dublin South West) is highly dependent because there are many young families who depend on child benefit," Mr Keaveney said.
In a sign of the post-Budget bitterness, Mr Rabbitte also said he had never witnessed the "calculated venom" that he had seen in the past few weeks from those no longer in the party. It is understood he was referring in particular to former Labour Junior Minister Roisin Shortall and rebel Labour TD Tommy Broughan, who both made highly critical speeches about Labour in the Budget.
But there is a strong sense of anger among party TDs at Mr Keaveney's move, with some complaining of his "betrayal", "giant ego" and "contradictions" by first voting for the social welfare bill and then voting against it 12 hours later. Party sources said that his departure had a "rallying effect" on the 33 backbench TDs left in the party. "He's got his headlines at all of our expense. But we're all over it already," one TD said.
Senator Lorraine Higgins told the Irish Independent that it took real political courage to stay in the heat of battle for the country's economic recovery.
"Simple solutions, fairytale economics and walking off the pitch is not the answer," she said.
But in a sign of the bitter rivalry between the pair, Mr Keaveney said that Ms Higgins was not in his considerations because she had been appointed to the Seanad and "doesn't have a constituency".
It is understood that Labour is going to hold off on removing Mr Keaveney as chairman until the New Year. "I'd say people are going to let the dust settle and look at the situation then," a party source said.
The party's options are extremely limited because his term does not expire until the next party conference expected in April at the earliest. Although disciplinary action can be taken against a member who brings the party into disrepute, Labour chief whip Emmet Stagg said Mr Keaveney had not done this simply by voting against the social welfare bill.
"I feel his position is untenable. It would be normal for him to resign the position," he said.