But while the Government seemed likely to push the bill through the House, the Greens are almost certain to use their hold on the balance of power in the Senate to crush the legislation in the Upper House.
About 40 MPs from all parties met earlier in the day to bring pressure on Gillard and Opposition Leader Tony Abbott to dump partisan politics and find a solution following the deaths of about 90 people in last week's disaster.
The debate took a more urgent turn as news of the latest sinking began unfolding. Three merchant ships and two Australian Navy vessels, supported by an Air Force P3 Orion carrying emergency liferafts appeared to have saved most of the passengers and crew pitched into the sea when their vessel sank.
Most are believed to be women and children.
At least one person has been confirmed dead. The authorities said that 125 people had been rescued, but as many as 150 may have been aboard when the boat capsized.
Federal Police received an emergency satellite call at 6.20am yesterday from the stricken vessel, putting its location seven nautical miles north of Christmas Island, but no trace could be found of it.
An hour later a second call was received, giving the location as 107 nautical miles from the island, sending nearby ships racing to the scene.
The first to arrive was a Philippines livestock carrier, MV Bison Express, which saw the boat slip beneath the surface and began rescuing survivors.
Two other merchant ships and the patrol boat HMAS Maitland followed, joined late in the afternoon by the hydrographic survey ship HMAS Leeuwin. Details of the rescue, including the numbers and nationalities aboard the boat when it sank, were still sketchy late yesterday.
There seemed little chance of a breakthrough on new legislation both major parties regard as essential to slow the flow of boats and to save lives at sea.
The Government diluted the tough border laws of former Liberal Prime Minister John Howard's Pacific solution, closing detention centres in Nauru and Papua New Guinea and ending other measures such as restrictive temporary protection visas. But as dozens of boats carrying thousands of asylum seekers resumed the dangerous crossing from Indonesia, Labor reversed its opposition to offshore processing and negotiated a limited refugee-swap deal with Malaysia.
The Opposition has consistently rejected the policy, which was struck down in the High Court because Malaysia is not a signatory to United Nations' refugee conventions.
Gillard said the time for party divisions on the issue had ended. "We have seen too much tragedy and I can't, and I don't believe other members of Parliament can now sit here with the prospect of more tragedy to come," she said.
But Abbott continued to reject the Malaysian deal, saying it failed to give asylum seekers the human rights protections demanded under the UN conventions. "This is a dud deal for Australia and a cruel deal for boat people," he said.
Abbott also noted the Greens' opposition to offshore processing of asylum seekers which, because of their grip on the balance of power in the Senate, would doom Oakshott's bill even if it passed the Lower House. Abbott instead advocated support for his private member's bill restricting offshore processing to countries party to the UN refugee conventions.
WHERE THE PARTIES STAND
Labor
* Wants to pass legislation to resurrect offshore processing and its Malaysian people-swap deal.
* Has offered to implement some Opposition policies, including reopening the detention centre on Nauru, if the Coalition votes for its bill.
* May be prepared to give more concessions if the Coalition returns to the negotiating table.
Coalition
* Supports offshore processing but staunchly opposes the Malaysian people-swap deal.
* Wants the Government to reopen Nauru, reintroduce temporary protection visas and instruct authorities to turn boats back to Indonesia when it is safe to do so.
* Is refusing to compromise or return to the negotiating table with the Government.
Greens
* Oppose all offshore processing.
* Advocate a more humane approach, including a near doubling of the refugee intake.
* Have proposed a multi-party committee to consider long-term solutions.
- AAP