A vote on the bill had been due Wednesday but it was rescheduled for May 16, because the lower house had not taken it up by the end of the day.
Homosexual activists hope to use the extra time for lobbying for the bill. The measure would allow homosexuals to transfer property and extend social security benefits and health plans to their companions.
"We have a list of deputies who do not have a clear position and we are going to work on them," said Beto de Jesus, president of the Gay Pride Parade Association.
If the bill is approved, Brazil would be the first country in Latin America to allow same-sex unions, as France and Australia do. The Netherlands already has legalized "marriage" between homosexuals. In the United States, only Vermont recognizes same-sex unions.
The bill was introduced in 1995 but has been modified to allow the extension of benefits to any kind of same- sex "partner" such as from brother to brother or granddaughter to grandmother, in order to try to ease opposition.
The prospects for passing the measure are not assured, especially because of religious opposition and because Congress is mired in investigations into allegations of corruption.