The Turnbull government’s hopes of changing race-hate speech laws appear doomed with Senate crossbenchers giving the move the thumbs-down.

Attorney-General George Brandis will this week bring to parliament changes to the Racial Discrimination Act that replace the words “offend, insult and humiliate” with “harass and intimidate”, setting the bar higher for complaints.

The Australian Human Rights Commission will be given power to head off frivolous claims at an early stage.

With Labor and the Greens opposed, the government is on the hunt for nine of the 11 crossbench votes.

Jacqui Lambie won’t be one of them; she says no one in Tasmania has approached her about the need to change the law.

The Nick Xenophon Team, which has three senators, has also signalled it won’t back a re-wording of Section 18C.

However, crossbencher Derryn Hinch says it’s a good step by the government.

At least four coalition MPs expressed misgivings about the changes when they were debated in a partyroom meeting on Tuesday, but they are not expected to cross the floor on the issue – AAP