Liberal senator Cory Bernardi plans to introduce a private bill this week to remove the words "insult" and "offend" from a contentious section of the Racial Discrimination Act aimed at making racial hate speech unlawful.
Section 18C makes it illegal to "offend, insult, humiliate or intimidate" someone because of their race or ethnicity.
Nationals senator Barry O'Sullivan believes there are about 18 or 19 coalition backbenchers who will vote for the change.
"We will just see what happens with it," he told reporters in Canberra today ahead of the new parliament being proclaimed.
"I think today will be a bit of a turbulent day one way or another."
Liberal colleague Chris Back insists words such as "intimidate" and "vilify" should remain, but the others should be removed.
"You could say anything to me, you could say 'I hate the West Coast Eagles' and I might be offended or insulted by that but you have the right to say that," he said.
Senator Back said it was an important issue which has been around a long time, but accepted budget repair was a higher priority.
Liberal Democrat David Leyonhjelm, who has also been pushing for the change along with fellow crossbenchers Bob Day and Derry Hinch, does not think there is any chance of success in the short term.
"It is a marathon, not a sprint," he said.
"But if you do not start you do not finish."
Independent Nick Xenophon, who wants 18C to remain as it is, doubts Senator Bernardi has the numbers to remove the words "offend" and "insult".
But he would accept a Senate inquiry.
"I think that a Senate inquiry process will be a good thing in terms of allowing a robust debate from both sides about section 18C," he said.
Greens Leader Richard Di Natale said Senator Bernardi's move was a big test for the prime minister.
"Unless Malcolm Turnbull takes on the extreme right in his party, shows some leadership, he will be remembered as one of the great failures in Australian politics," he said.
Independent senator Jacqui Lambie wants the Act to be left as is.
