Labor is hoping crossbench senators will join its fight against the Turnbull government's changes to citizenship rules.
The overhaul, which includes a tougher English language test and longer waiting times for aspiring citizens, passed parliament's lower house on Monday.
Labor has labelled the measures unfair and divisive, disagreeing with claims they are - in part - being introduced in the name of national security.
The United Nations' High Commissioner for Refugees has also raised concerns that the changes may fall foul of international conventions.
The government, however, insists the move is in the nation's best interest, arguing Australian citizenship is a privilege, not a right.
The opposition's immigration spokesman Tony Burke said the government is refusing to listen to concerns about the proposal.
"The campaign will now turn to the Senate to encourage the crossbench members to listen where the government has refused to do so," he said.
The Nick Xenophon Team, which has three senators, has already flagged opposition to parts of the legislation.
A Senate committee is investigating the bill, with a report due by September 4.
