The bill, which proposes a wide-ranging inquiry into banking, insurance and superannuation, easily has the numbers to pass the Senate but to be debated in the lower house, an absolute majority of 76 votes are needed. Labor and the crossbench have 74 votes in the lower house, meaning two Coalition votes are needed to enable debate.

Once this has occurred, only a simple majority is needed to pass the bill. Even if Barnaby Joyce and John Alexander were in the Parliament the bill would still pass by 76 votes to 73 if Mr O'Brien and Mr Christensen voted for its passage.

Both Mr Joyce and Mr Alexander are fighting byelections and will be absent next week when the House sits for the final week of the year, leaving the Coalition with a maximum 73 votes to Labor and the crossbench's 74, meaning the bill could pass easily. It would pass by 76 votes to 71 votes if if Mr O'Brien and Mr Christensen voted for its passage and Mr Alexander and Mr Joyce were absent.

Mr O'Brien's new terms of reference will have the commission of inquiry look at the discrimination against people with mental health issues by insurance companies and other financial service providers.

He and Mr Christensen are likely to formally commit to supporting the bill when the Nationals discuss it at their party room meeting on Monday next week.

Senator O'Sullivan intends to have the Senate debate and pass his bill later this week after it has dealt with same-sex marriage. Sources said the government may filibuster on same-sex marriage to try to delay the bank ambush. But the Senate could still pass the bank bill early next week, and there would be a slim chance it passes the House of Representatives before it rises at the end of that week for Christmas.

A commission of inquiry is effectively the same as a royal commission but is established by the Parliament, rather than the executive, and will report to the Parliament, not the executive.

The bill proposes three commissioners – a former judge, a community representative and a financial expert – who would all be appointed by the Senate.