The legislation would send all asylum-seekers arriving in Australia by boat to countries like Nauru for processing offshore.
The government hoped to force a debate on the draft laws in parliament today, despite a Coalition-dominated Senate committee recommending they be scrapped.
The Prime Minister, John Howard, says he and his immigration minister are still negotiating with the backbenchers concerned.
“How I conduct negotiations, and in this case my minister, Amanda Vanstone, with our parliamentary colleagues - I'm not going to go into the detail of those discussions except to acknowledge there are discussions and we're working through some areas of difference,” Mr Howard said.