A coalition of politicians, writers and artists is trying to persuade ministers to accept changes made by peers to the Racial and Religious Hatred Bill.
Rowan Atkinson says religions should defend themselves
Demonstrators are expected outside Parliament when the bill returns to the Commons on Tuesday after being substantially amended in the Lords.
Peers voted to restrict terms of the bill to threatening words or behaviour.
But ministers want it to include insults and abuse, which critics say could unfairly target comedians.
'Right to criticise'
At a press conference on Monday, comedian Rowan Atkinson, who has been a prominent critic of the bill, said: "No one deserves a right to freedom from criticism."
Government attempts to include an offence of being "reckless" about stirring up hatred could affect performers, he added.
Mr Atkinson said of artistic work: "If it generates dislike of that religion's followers, they need to accept that.
"They cannot deny responsibility for their practices. They should defend them, justify them or amend them."
Under the proposed law, the offence of inciting racial hatred would carry a maximum prison sentence of seven years.
Last year, peers voted by a majority of 149 in favour of a cross-bench move to implement freedom of speech safeguards.
These include making sure nobody is found guilty of religious hate crimes unless it is proved they intended to stir up hatred.
Only "threatening words" should be banned by the bill, not those which are only abusive or insulting.
Labour backbencher Bob Marshall-Andrews said the legislation was "going to have a chilling effect on not just religion but on the whole spectrum of freedom of speech".
He said he did not know how many of his party colleagues would vote against the government but that many would "make their minds up very, very late".
Liberal Democrat human rights spokesman Evan Harris said Tuesday's vote on the bill would be parliament's last chance to protect free speech.
"These freedoms to speak and to argue, to criticise and indeed to ridicule, once lost, are very rarely got back.
"And I think it will be a sad day if the opposition parties and indeed some brave backbench Labour rebels are not able to defeat the government and maintain the House of Lords' position on this bill. "
He said the new law would create a "chilling effect that would stifle free expression".
Shadow attorney general Dominic Grieve said his party would do "everything it can to work with others in parliament to remove the worst parts of the governments' proposals".
However, ministers reject claims that the current bill would stop free speech.