CANBERRA, June 19  - With parliament due to rise at the end of the week for the long winter break, the coalition needs 10 extra votes to pass its legislation which will bring in needs-based funding for schools and roll out an extra $18.6 billion in funding over the next decade.

Education Minister Simon Birmingham has offered a compromise to the Greens that includes reducing the rollout timetable from 10 years to six, more accountability over state government funding, and an independent watchdog.

Greens education spokeswoman Sarah Hanson-Young said that addressed their fundamental concerns.

Shortening the funding rollout period could boost the existing package by $5 billion.

Greens members met briefly in Canberra on Monday but will hold a longer meeting on Tuesday, ahead of the Senate debating the bill on Wednesday.

If the government gets the Greens on board only one other crossbench vote will be needed.

However, Labor and the Australian Education Union - which notched up at least $7 million in political expenditure in the past financial year and has directly targeted crossbench senators in protest action this year - say the deal is not good enough.

"There is no way the Labor party will support $22 billion worth of cuts to our schools," Labor leader Bill Shorten told reporters in Canberra on Monday.

"You just have to talk to everyone from the education union through to the National Catholic Education Commission."

Retiring Liberal senator Chris Back, who leaves parliament at the end of this week, is upset Catholic schools will lose out under the package.

Senator Birmingham insists the Catholic sector will get an extra $3.4 billion over the next decade, but department figures given to Senate crossbenchers show that's about $4.6 billion less than under existing arrangements.

Senator Back, who served with the Catholic Education Commission before entering parliament, wants a year-long inquiry into the way parents' capacity to pay is calculated.

"I am not satisfied yet that the change ... will do anything other than radically hurt the Catholic system in Australia and if that's the case I can't support it," he told reporters in Canberra.

Nevertheless, he believes the minister is doing a good job in untangling the mess of school funding and is confident the issue can be sorted.

Senator Birmingham said his discussions with Senator Back were about some "technical issues" affecting the Catholic sector.

"I'm confident we'll have support within government ranks. Chris is a good man," he told reporters.

The government appears to have had better luck with One Nation, which can deliver four of the 10 or possibly 11 votes the government will need in the Senate.

The party's whip Brian Burston has told The Australian its senators would support Gonski 2.0.

The Nick Xenophon Team has similar concerns to the Greens, with education spokeswoman Rebekha Sharkie saying the compromise has potential to create a "truer version of Gonski".

"Fingers crossed we can do what we should be doing and that's working together for the best for our children," she said.

A vote may be delayed until August when parliament resumes and a replacement for Senator Back is in place.