The electricians' union says it will not relent in its attacks on crossbench senators over anti-union laws.

Centre Alliance's Rex Patrick and Stirling Griff, along with independent senator Jacqui Lambie have been hounded over the Morrison government's “ensuring integrity” bill.

The powerful trio have been singled out in newspaper advertisements, and Senator Patrick says he is unwilling to discuss other legislation with unions if the campaign continues.

Electrical Trades Unions national secretary Allen Hicks says such campaigns are one of the major reasons that unions exist.

“We are in a pitched battle to prevent the worst piece of anti-union, anti-worker legislation this country has ever seen, all at a time when wage theft is rampant and incomes are stagnant,” he said.

“Senator Patrick has a pivotal role in whether this bill is passed and becomes legislation. We have every right to question his judgment and other decision makers, in a robust fashion.”

The Centre Alliance says it will only support the legislation if the government changes it.

Senator Lambie says she will consider the bill only if high-profile Victorian construction union boss John Setka resigns.

Industrial Relations Minister Christian Porter says he is open to Centre Alliance amendments that would scrap a public interest test for union mergers.

Senator Patrick is pushing for a demerit point system so that officials are not banned for minor breaches. He also wants to prevent employers from being able to apply for union de-registration.

Still, the ETU and the Australian Council of Trade Unions want crossbench senators to block the draft laws outright.

“This legislation is an abomination. We are deeply opposed to it in its entirety,” Mr Hicks said.

“While we welcome Senator Patrick's concerns, his amendments simply put lipstick on a pig.”

The legislation should come before the Senate before the end of the year. The government needs the support of four out of six crossbenchers to secure its passage.