The Turnbull government faces what could be its first defeat in the Senate over a motion backing a banking royal commission.

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.

Labor Senate leader Penny Wong has flagged the opposition's intent over a Senate motion on a banking royal commission that enjoys enough support to ensure its success. Credit:Graham Tidy

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.