Key crossbench Senator Jacqui Lambie says she might vote for a controversial bill to facilitate the deregistration of unions and officials if John Setka remains at the helm of the Victorian division of the CFMEU.

With Labor resolved to opposing the Ensuring Integrity Bill, which the government says is necessary to deal with rogue unions and officials, the decision now rests with the Senate crossbench, which is being lobbied by both sides of the argument.