The Morrison government may have to agree to further concessions to secure the passage of legislation enabling the easier deregistration of unions and officials, with both One Nation and Jacqui Lambie yet to be convinced.

Senator Lambie has said previously that she would vote for the bill if John Setka remained at the helm of the Victorian division of the CFMEU, but she is also concerned the laws could lead to the deregistration of non-militant unions such as the Nurses Federation for administrative errors.