The Government and Qantas both want the same arrangements that allow Virgin's domestic business to be majority owned by state-backed Etihad, Singapore Airlines and Air New Zealand. Its international arm is majority owned by Australians.
Qantas is bound by acts that restrict foreign holdings to 49 per cent and require the airline to keep its head office and main maintenance, training, administration and catering operations in Australia.
While Qantas sees the repeal of those acts as a longer-term benefit, it sought an immediate boost through a loan guarantee facility. Abbott instead said opening the airline to foreigners was the only option.
This would require Qantas to break its operations into two: a domestic business open to all comers, and an international arm still majority owned by Australians to ensure national carrier status and international landing rights.
Labor would have supported a loan guarantee and was prepared to negotiate changes to laws that place restrictions on foreign individual and airline holdings.
But it has rejected Abbott's plan and, with the Greens, will block proposed legislation in the Senate.
The new Senate, which sits from July 1, will also be problematic. The Palmer United Party, with a probable three votes, independent Nick Xenophon and the Democratic Labour Party oppose the plan.
"The interesting thing is that the Labor Party's answer here appears to be a subsidy," Abbott said.
"We want to give Qantas its freedom, they want to give Qantas a subsidy. We want to give Qantas a hand up, they want to give Qantas a handout."
Abbott has tried to blame Qantas' woes on the carbon tax - which he has so far failed to repeal in the Senate - although Qantas has said its present problems "are not related to carbon pricing".
Hockey has also conceded the Government has no fallback plan: "Plan B is to improve the economy. That's what we have to focus on."
The Government remains vulnerable on jobs. Abbott has conceded Qantas will move work overseas if the law is changed, sparking angry retorts from Labor and unions and warnings that with flow-on effects more than 100,000 jobs were at risk.
"Tony Abbott has created a new export industry - Australian jobs," said Opposition leader Bill Shorten.