The Cabinet discussed the dilemma before Parliament and the Labor caucus was meeting late yesterday with no clear indication of what Gillard intends doing now.
Although no Labor MPs are expected to cross the floor if Gillard sticks to her guns, a number are opposed to any policy of overseas processing of asylum seekers.
Others want to avoid defeat on a major issue for a Government whose popularity hovers at record lows.
The Migration Act amendments follow the Government's abandonment of its previous rejection of key measures of former Liberal Prime Minister John Howard's Pacific solution, including overseas detention and processing to deny asylum seekers access to the Australian legal system.
Spurred by a continuing increase in the number of boats arriving from Indonesia, overcrowded facilities on Christmas Island, riots and hunger strikes, and popular anger at her failure to find an answer, Gillard arranged the exchange deal with Malaysia.
Under the agreement Australia would send 800 asylum seekers to Malaysia and accept 4000 United Nations-accredited refugees.
But the deal was struck down by the High Court in a decision that also excludes the reopening of the Pacific solution detention centres on Nauru and Manus Island in Papua New Guinea.
The proposed amendments would allow successive governments to take what they regard as the best action on asylum seekers, including Nauru, rejected by Gillard.
But Abbott has scented blood and will accept only Nauru on the grounds that it is, unlike Malaysia, a signatory to UN refugee conventions.
Yesterday the Government refused to call its promised vote on the amendments, citing the Opposition's demand for its long list of MPs to be heard.