The Taoiseach is urging Senators to tow the line and vote for the Social Welfare Bill so cuts can be implemented from the start of the year.
A number of Labour Senators and even some of those appointed by the Taoiseach himself have threatened not to support the Bill.
The full group of Labour Senators are demanding to meet the Minister for Social Protection tomorrow.
Labour Minister Pat Rabbitte has also called for discipline among the Senators in his party who are considering voting against the Social Welfare Bill in the Dail.
At least 4 Senators have expressed reservations about supporting the Bill which begins its passage through the Seanad tomorrow.
The Coalition has a tight majority in the Seanad with only 31 of the 60 members.
A number of Labour Senators and even some of those appointed by the Taoiseach himself have threatened not to support the Bill.
The full group of Labour Senators are demanding to meet the Minister for Social Protection tomorrow.
'Vigorous debate within the party'
Minister Rabbitte says the Senators need to show discipline.
"As well as robust debate and nurturing vigorous debate within the party...we have to have discipline" he said.
"If discipline breaks down, then you are no more than a flag of convenience - and that's not the position of the Labour Party, the oldest party in the State founded in 1912".
"Yes there are differences - but it's a broad church" he added.
While Taoiseach Kenny says he is hopeful that those who should support the Bill in the Seanad will.
He was speaking at an event for the Association of European Journalists in Dublin today.
The Taoiseach says clearly he does not speak for any individual Senators and he says it is time to "move on".
"Obviously it's a matter for any individual to decide what they want to do. I would hope that the Social Protection Bill will be voted through by the Senate and that we move on to making the applicable pay rates early in the new year," he added.