Prime Minister Malcolm Turnbull's plan to use Senator Bob Day to convince fellow Senate independents to reinstate the building industry watchdog appears to have slammed into a brick wall.

Mr Turnbull wants South Australian Family First senator Bob Day, a longtime friend, to convince six crossbenchers to support the Australian Building and Construction Commission (ABCC) legislation when it goes before the Senate.

He said he'd consider their reasonable amendments.

But it appears he may have to deal with each crossbencher individually if he wants their support.

Independent senator Jacqui Lambie said she would only support a national anti-corruption body that covered not just construction but banking, insurance and government officials.

"Bob Day is free to make decisions for himself and his own state - but the problem for Bob is that his voting record shows he should just join the Liberal Party," Senator Lambie said.

Liberal Democrats senator David Leyonhjelm said the idea that Senator Day could round up six crossbench votes was insane and Senator Day would agree.

"That's not how you do it on the crossbench ... we'd be lucky to agree on what day it is," he told Sky News.

Independent senator Glenn Lazarus accused Mr Turnbull of attempting to "sweeten up" other crossbenchers.

Palmer United Party senator Dio Wang said he had received a "cold" response from the government to his ideas in recent weeks, despite earlier signs of listening.