CANBERRA, June 15 - After successfully gathering support to pass changes to vocational education and child care over the past six months, the minister is now at the crunch point on his Gonski 2.0 model.
The new package will put an extra $18.6 billion into schools over the next decade and, the government argues, distribute federal funding on a true needs basis.
Labor is staunchly opposed, largely because the plan is $22 billion less than its own pledge for schools.
Its opposition means the government must find 10 crossbench senators to support its plan.
Senator Birmingham says - as he has about his previous reforms - the government will be pragmatic in its negotiations, but won't let them play out in public.
"We will obviously hear the cases and requests from different crossbench parties," he told reporters on Thursday.
"That doesn't mean we agree with all of them, but we will work cooperatively to get the legislation through."
It's understandstood he met with the Greens on Thursday, who hold nine crucial votes and have offered conditional support.
The minor party is demanding underfunded schools get an increase in funding faster than the government's proposed 10 years, requirements to "tie" states to the reforms to make them boost their own funding to public schools, and an independent national schools resourcing body to oversee all aspects of schools funding.
The Nick Xenophon Team of three wants similar changes.
Senator Birmingham wouldn't reveal how much it might cost to shorten the time-frame, saying it depends on what assumptions are used.
Independent senator Jacqui Lambie isn't supportive at this stage, specifically citing the need to make sure the states do their part.
Liberal Democrat David Leyonhjelm says some of the Greens' proposals made sense in light of the "distinct danger" states will try to shift costs.
Previously he's opposed the government's package because of his belief no more money should be put into schools while the budget is in deficit.
The legislation will be debated in the Senate next week and Senator Birmingham hopes to have it passed by the time parliament rises on Thursday for the long winter break.