Mr Murphy was convicted on nine charges relating to tax evasion yesterday
A Labour Senator claims the conviction of prominent republican Thomas 'Slab' Murphy is " suffocating" the Sinn Féin party membership.
Party leader Gerry Adams is under pressure to distance himself from Murphy, who was convicted yesterday.
Murphy was found guilty of nine charges by the Special Criminal Court. He was remanded on continuing bail ahead of a sentencing hearing in February.
The 66-year-old, who lives at Ballybinaby, Hackballscross in Co Louth, did not file returns for his farming activities between 1996 and 2004
Mr Adams has previously insisted that Thomas Murphy is a "good Republican".
While in a statement yesterday, Mr Adams said: "I have no comment to make until the legal process has been concluded".
But Labour Senator Mairia Cahill told Newstalk Lunchtime that is not good enough from the Sinn Féin leader.
Daniel McConnell, political editor of the Irish Examiner, believes the Sinn Féin president will be under pressure to clarify his position ahead of the general election.
"And will he move to distance himself as Sinn Féin are looking for a more middle class vote heading into the election. They are trying to broaden the party's appeal", he said.
"They are essentially on the march towards power, but a lot of people feel that as long as they continue to have links with people who have been now convicted of very serious charges, their commitment towards democracy and the rule of law in this country remains questionable".