Crossbench MPs believe they have the numbers in both houses of parliament to force the prime minister to hold a commission of inquiry into the banks.
They are even threatening to block this year's budget if Malcolm Turnbull and his government ignore the will of the people.
Queenslander Bob Katter says it would amount to a "constitutional crisis".
"They have got to get a budget through later this year - they want to play that game, fine let's play it," Mr Katter told reporters in Canberra on Monday.
Tasmanian MP Andrew Wilkie, agreed that the government rejecting an inquiry would represent a "collapse in democracy".
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"That's evil behaviour," he told a joint media conference with Mr Katter, Greens MP Adam Bandt, NXT's Rebekha Sharkie and independent MP Cathy McGowan.
Earlier Mr Katter and Mr Wilkie introduced to parliament separate private bills calling for greater scrutiny of the banking sector.
Mr Katter's bill would establish a commission of inquiry into the banking and financial services sector, specifically looking at unethical, unlawful and improper conduct.
It would have the same powers as a royal commission, as well as additional powers relating to the protection of whistleblowers.
Mr Katter criticised politicians who had run away from the issue but praised the "courage and intellectual integrity" of Nationals MP George Christensen, who sat with the crossbencher on Monday in support of the bill.
"Everyone agrees to this except the Liberal Party ... and their isolation is standing out now like a neon light," Mr Katter told the lower house.
He told reporters there have been 38 inquiries in the last seven years which have achieved "absolutely nothing".
Mr Wilkie's proposal would make an existing voluntary code of practice mandatory and give the banking regulator more power to issue penalties for breaches.
"It would give banking customers some rights when dealing with their financial institutions," he told MPs.
It's the second time Mr Wilkie has tried to put forward such laws, having made an attempt in 2012 under Labor.
He told reporters the government is "completely and utterly" out of step with the community.
He said the House of Representatives review into the big four banks once a year is a "nonsense response" to a significant problem.
Last week, the Greens introduced a bill in the Senate to establish a similar commission of inquiry.
The proposal has the support of Labor and most of the crossbench, as well as Nationals senator John Williams who vowed to cross the floor.
