Labor has vowed to keep fighting the Turnbull government's school funding package until the very last vote in parliament.
The government is on the verge of victory after securing the 10 crossbench votes it needs to legislate the so-called Gonski 2.0 deal.
The Senate faces another late night marathon on Thursday, with the government forcing senators to stay behind until the package is passed.
Labor education spokeswoman Tanya Plibersek indicated the opposition could drag debate out for a very long time.
"This is an unfair deal and we will fight it to the last," she told reporters in Canberra.
"While there's life there's hope. We'll be continuing our discussions with the crossbench until the very last minute, until all of these amendments are voted on and until we get to vote on the legislation itself."
The new deal, negotiated with crossbenchers, will mean schools receive an extra $5 billion over the next 10 years, lifting the total funding boost to $23.5 billion.
Under-funded schools will reach funding targets in six years instead of 10 and $50 million will be spent on a transition fund for Catholic and independent schools over 12 months.
The government has also agreed to a new watchdog conducting a review of the schooling resource standard, which is the basis of the new needs-based funding model, and a guarantee the states won't withdraw their funding as more federal money flows through.
These concessions helped to secure support from the Nick Xenophon Team.
They are similar to demands from the Greens, with education spokeswoman Sarah Hanson-Young claiming credit for securing a better deal for public schools.
Despite that, the minor party's nine senators won't vote for the bill because of the transition package for Catholic and private schools.
Neverthless, NXT education spokeswoman Rebekha Sharkie said the Greens deserved some kudos for the government's compromises.
"We both agreed where we saw the flaws in the package and I think we both had very similar views on where we thought it needed to get to," she told ABC radio.
"They certainly do (deserve some kudos) and I hope that they'll vote for what's being put forward in the parliament now."
The National Catholic Education Commission is still urging the Senate to reject the package, saying a meeting with Education Minister Simon Birmingham on Wednesday night failed to ease its concerns.
