The Turnbull government is facing internal divisions over its Gonski 2.0 legislation as the Catholic sector and the Australian Education Union launch a fierce eleventh hour lobbying campaign against a shake-up of Australia’s schools funding model.

Politicians’ offices received calls from public school teachers telling them to block the package, while the Catholic sector called on parents to contact their local MPs and “say no to Catholic education cuts”.

In the lead-up to this week’s Senate vote, the National Catholic Education Commission has set up a campaign website and taken out a full-page ad in The Australian newspaper, and Catholic schools are sharing slick new video ads with parents on social media.

One of the ads, which features a teacher addressing a classroom of parents, portrays the Gonski 2.0 legislation as a threat to school choice.

Also on Monday, the Australian Education Union held a ‘day of action’ as part of its ‘I Give A Gonski’ campaign that has previously included television and billboard ads.

Both groups are piling pressure on the government and Senate crossbenchers as Education Minister Simon Birmingham tries to shepherd the package through the Senate in the final week before the winter break.

The government was dealt another blow on Monday when Coalition MPs Kevin Andrews and Chris Back both expressed reservations about the package.

Retiring Senator Back, a former WA’s Catholic schools administrator, suggested he may cross the floor, while Mr Andrews raised concerns about working with the Greens.

Those divisions will come to a head when the Coalition party room meets on Tuesday to debate the education package.

Simon Birmingham has stared down a campaign from the Catholic sector. Photo: AAP

Education Minister Simon Birmingham said he was still confident the package had the support of his colleagues, arguing it was vital the legislation passed this week.

“Because it’s important for Australian schools who are budgeting for next year, over the coming months, to have the certainty in terms of their school funding for next year and beyond,” he said.

The government needs the Greens’ nine votes, plus one more senator, or it would have to win the support of a more diverse group of 10 crossbenchers.

Greens leader Richard Di Natale said his party was willing to block the package and continue negotiating when Parliament returns.

“The primary consideration is getting it right. It could be dealt with this week, but you want to get it right,” he told Sky News.

But he said the government appeared open to ceding ground on the Greens’ three demands.

The minor party says extra funding is needed to lift schools to their funding target sooner, the package must ensure state governments also fulfil their obligations, and an independent body should be set up to monitor how schools funding is spent.

It has been suggested that the Greens’ reluctance to back the changes stem from the Australian Education Union’s fierce opposition to the package.

But Senator Di Natale brushed off concerns the union might campaign against his party at the next election.

“I’m confident that ultimately if all of the elements are what it takes to fix this mess … the key stakeholders in this space would welcome that,” he said.

One Nation’s four senators and independent Derryn Hinch also indicated on Monday that they were likely to support the package.

The government says the new model will inject $18.6 billion into the school system over 10 years while ending “special deals” negotiated by Labor.

But the Catholic education system has claimed the funding distribution means a cut for its schools, while the opposition and the AEU says the package rips out $22 billion, compared with arrangement negotiated by Labor.