The government needs the vote of either One Nation or Senator Lambie to pass the bill,which will make it easier to deregister unions and disqualify officials who breach workplace laws.
Senator Hanson said the amendments she had negotiated with Attorney-General Christian Porter would"minimise the risk"of unions being deregistered over paperwork breaches.
She said if workers or unions"want to be upset with anyone this week"it should be Labor and the Coalition government,who passed free trade agreements that would allow more foreign workers to come to Australia.
Senator Lambie,who has threatened to vote for the bill if Construction,Forestry,Maritime,Mining and Energy Union Victorian secretary John Setka did not resign,said she was"not prepared to throw every single union member in the country under the bus just because one bloke wants his job".
She circulated amendments she said would ensure no union official could be disqualified,or union deregistered,for failing to lodge forms in time;that workers'right to strike would be protected;and that no court could block a union merger.
"The scale of bad behaviour in the union movement should be reflected in the scale of the penalties the bill applies,"Senator Lambie said.
"The government's bill treats all unions like they're all the same part of the problem,and that's just not the case. Teachers,nurses and firies aren't the problem."