NDP finance critic Nathan Cullen is leading the charge, writing committee chair James Rajotte, a Conservative MP, to request the meeting and the appearance by the finance minister.
In his letter, Cullen notes the revised budget projections by the parliamentary budget officer that suggest Canada will see a $1-billion deficit at the end of the year.
"This is a significant deviation from the Budget 2015 estimate of a $1.4 billion surplus," wrote Cullen, the committee's deputy chair.
"I believe it is important for parliamentarians to examine the impacts of this dramatic shift in government finances and the weakening Canadian economy."
Parliament's standing orders, or rules, require a committee chair to call a meeting within five days of getting requests from any three members of the committee. The MPs need 48 hours' notice, so the earliest the meeting could happen is Tuesday, according to the NDP.
The NDP's other finance committee members, Pierre Dionne Labelle and Raymond Coté, have also requested a meeting.
While the rules say the committee has to meet once three members make the request, it's not a given that Oliver would have to appear.
Read Nathan Cullen's letter to James Rajotte.