Earlier on Wednesday, the government headed off a lower house motion, introduced by Labor, which would have embarrassed the Coalition over the issue - but would not have forced a commission to be held.

A similar motion is set to be debated in the Senate on Thursday and looks likely to succeed, underscoring the fact that the government cannot control the agenda in the upper house, where it holds just 30 of 76 seats.

The government was also embarrassed on Wednesday when it emerged its so-called $6 billion omnibus savings bill contained a $107 million accounting error that overestimated the amount of money that would be raised. The error was made by Treasury.

Labor Senate leader Penny Wong flagged the opposition's intent on the banks motion and it enjoys the support of independents Jacqui Lambie and the Nick Xenophon team, the quartet of One Nation senators as well as the Greens over the matter - which potentially delivers the votes needed to pass the motion.

The crossbench senators also have amendments planned of their own, including widening the motion so that it calls for an inquiry into political donations by the banks.

While Labor looks likely to have spearheaded the government's first defeat, the motion will not force the government to actually hold the inquiry.

But a loss this early in the 45th Parliament will create political embarrassment for the government, which has already been blind-sided by 13 senators from its own backbench and seven crossbenchers teaming up to push for changes to be made to section 18C of the Racial Discrimination Act, despite Prime Minister Malcolm Turnbull's repeated statement there are "no plans" to amend the legislation.

Coalition MP George Christensen - who has advocated for a royal commission - headed off the opposition with a counter-motion in the House, which left Labor's proposal dead in the water.

Instead, the Government announced a new inquiry into bank's small business lending practices, a move which potentially could lead to further regulation down the track.

Opposition Leader Bill Shorten, continuing the theme he had carried through the election campaign, labelled Mr Turnbull the "lunchtime warrior who gives Westpac a lecture" while arguing for the motion to be passed in the lower house, claiming that "you get the sense here that the government will do anything and everything, say anything and everything to avoid a royal commission into banks".

"Every Australian uses a bank, but too many Australians are being used by their bank. Now, the government knows there is a problem...we have to acknowledge that there have been too many troubling incidents over recent times for them to be simply be dismissed," he said.

Mr Shorten was backed by independent Bob Katter, who railed against the major banks in an at-times contradictory speech that included the observation that he would "have to live until the day I die".

But Mr Christensen blocked the move, with a motion which acknowledged community concerns over bad behaviour from the banks, while at the same time, noting Mr Shorten had been financial services minister when many of the scandals which have captured the public's anger, first emerged.

Mr Christensen also pointed to the changes the Turnbull Government had wrought following the Murray review into the financial system, which included bolstering ASIC's resources and forcing banking chiefs to front a parliamentary committee annually,

The Member for Dawson said a royal commission would "signal internationally that there are structural problems with our banking and financial system, which would have significant repercussions for confidence, international investment and for our AAA credit rating."

Australian Bankers Association chief Steve Münchenberg again criticised Labor's move to set up the inquiry and insisted the banks were moving to address community concerns.

"There have been issues and we are working to fix those with our industry reform package we released in April," he said. "Banks are also addressing community concerns about bad apples moving around the industry, the handling of customer complaints and the treatment of whistleblowers."

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