Mr Liam Lawlor has been urged to step down as vice-chairman of the Oireachtas Finance and Public Service Committee ahead of a vote to be taken on his position tomorrow.
Independent senator Mr Joe O'Toole, who would have the deciding vote on a motion of no confidence in Mr Lawlor, has written a letter to the Dublin TD urging him to stand down.
"I do not believe that the matter of your position as vice-chair should go to a division of the committee. It would certainly not be edifying that it should become political or break along party lines," said Senator O'Toole in the letter.
Mr O'Toole said he appealed to Mr Lawlor in the interests of all Oireachtas members to step down "at least until your difficulties in another place are resolved".
The Government chief whip, Mr Seamus Brennan, expects to meet Mr Lawlor ahead of tomorrow's meeting but said last night the meeting had not yet been possible because Mr Lawlor had been busy in the High Court.
The Progressive Democrat committee representative, Senator John Dardis, has indicated that he would vote to support the Fine Gael-tabled motion.
The Government, with the support of Mr Lawlor and Mr Denis Foley, would have had a majority of one on the 19-member committee. However, Mr Dardis's indication that he would support the motion means the balance is in the hands of Mr O'Toole.