Several Green Party councillors have voiced criticism of the suspension of Dublin Central TD Neasa Hourigan from the parliamentary party, and her removal from Oireachtas committees, for voting against the Government on the eviction ban.
The Greens took decisive action against the deputy, including taking away her positions on Oireachtas committees.
The TD had been chairperson of the budgetary oversight committee.
Cork Councillor Oliver Moran said on Twitter: "Gravely disappointed at the decision of the Green Party PP to sanction Neasa Hourigan last night. Taken without due notice, while Neasa was chairing an Oireachtas committee and so unable to be at the meeting. Length and severity of the sanction is gratuitous and self-defeating."
Cork Councillor Liam Quaide tweeted: "Our parliamentary party has got its values tragically askew."
Another Cork councillor - former TD Dan Boyle - said on Twitter: "I feel the length of the suspension given to Neasa Hourigan is too long and she should be allowed to retain her committee memberships where she does excellent work. I hope a mechanism to appeal these elements exists."
A Green Party minister said the decision to suspend Deputy Hourigan was not easy or comfortable.
However, Minister of State at the Department of Agriculture Pippa Hackett said that Ms Hourigan is a Government TD and that means voting with the coalition on difficult issues.
"We have to vote through the easy votes and the tough ones too," Senator Hackett told RTÉ's Morning Ireland.
The Green Party said it regretted having to take these steps, but said effectiveness in Government relied on unity in every vote.
This means the Government now has a majority of just one and so discussions with Independents TDs are likely again ahead of next week's no confidence motion in the coalition tabled by the Labour Party today.
However, one of the changes it agreed with the Regional Independent Group, to allow people in nursing homes to retain all income from renting their home, is causing concern among some in Government.
Minister Mary Butler, who has responsibility for older people, fears it could lead to what she called the premature entry of people into nursing homes.
The no confidence motion will be debated and voted on in the Dáil next week.
Minister Hackett said the Government numbers are "secure" ahead of the vote.
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No 'formal' deals with Independents - Taoiseach
The Taoiseach said there were no "formal" constituency deals with Independents in return for their support in last night's Dáil vote.
Speaking in Brussels, Leo Varadkar said: "We are a coalition Government, we do have a majority, but there are a number of Independents who vote with us a lot of the time. And that helps to give us an even more secure majority than we would have without them.
"There is an ongoing engagement with Independents on constituency issues but no formal agreement in that sense."
Mr Varadkar said that he had not personally discussed next week's vote of confidence in the Government with Independent TDs.
"This isn't the first motion of confidence we've had in the Government or in a Government minister. There’s one every two or three months. It will be defeated, it will be defeated by a significant margin. It is largely political theatre."
He said that, as with previous governments, the coalition would speak to "like-minded Independents" who do not want an election next week or in three weeks' time.
"There are sensible, reasonable Independents and we would talk to them about issues that are of concern that we’d have, on national issues and consistency issues, just as we do with our own TDs. That's not forgotten or over backbenchers. So there's nothing unusual about that."
Mr Varadkar added: "Let's not forget what a motion conference means. That means an election in four weeks' time. Does anyone really think that's going to solve any of our problems? I don't think so."
Additional reporting Mícheál Lehane and Tony Connelly
