Irving Gerstein declined to give up his role as the committee's chair after Liberal Senator Céline Hervieux-Payette argued he should step down.
Liberal Leader Justin Trudeau said Gerstein seems to continue to have the confidence of Prime Minister Stephen Harper.
An auditor with Deloitte, which performed the forensic investigation on Duffy's $90,000 in questionable expenses, confirmed last week that Michael Runia, one of the firm's executives, called him to ask how much Duffy owed.
RCMP documents allege Gerstein contacted Runia about the Duffy audit. Gary Timm, the auditor who Runia phoned, said he didn't give Runia any information and ended the call as quickly as possible.
Senators will vote at 5:30 p.m. ET on whether to force the internal economy committee to hear from Runia. Last week, the committee voted not to debate a motion to call Runia and Gerstein.
The controversy over emails from a former lawyer in the Prime Minister's Office regarding the Senate scandal continued as MPs emerged from weekly caucus meetings.
MPs are usually fired up once they hit Wednesday question period at 2:15 p.m. following a morning of meeting with colleagues and hearing from their respective party leaders.
The opposition has kept up the heat on the governing Conservatives following a year-long Senate spending scandal.
Over the weekend it was revealed the Prime Minister's Office still had emails, thought to have been deleted, sent by former PMO lawyer Benjamin Perrin.
RCMP documents show that police believe Perrin knew about a deal between Prime Minister Stephen Harper's former chief of staff, Nigel Wright, and Senator Mike Duffy, for Wright to pay off Duffy's $90,000 in questionable expenses.