With Labor opposed to the controversial new funding model, the government is still short of the numbers needed to overhaul the way the nation's schools are funded.

Education Minister Simon Birmingham will bring his school funding legislation to a Senate vote over the next two weeks, before Parliament rises for an extended winter break.

The government is moving quickly on the issue because the changes would take effect next year and principals need certainty to plan their budgets.

The government's proposals have infuriated the Catholic school sector in particular, which will launch a last-ditch bid to torpedo the new funding model.

Having been unsuccessful so far in getting the government to water down its changes, the Catholic sector will shift its focus to the Senate crossbench.

Fairfax Media understands Catholic eduction authorities will write to the Senate crossbenchers outlining their concerns with the new model and how it would affect schools in their state.

According to the National Catholic Education Commission, 40 per cent of its schools would be worse off under the government's plan.

Unlike Labor, the Greens have not reached a reach a final position on the new funding model and have been careful not to rule out voting with the government.

But Greens education spokeswoman Sarah Hanson-Young has insisted the government shorten its 10-year funding timeframe so money flows more quickly into disadvantaged public schools.

The Greens also want the government to commit to create an independent schools resourcing authority, as recommended by the Gonski review, to take the politics out of school funding.

If the Greens vote against the government, it would need to win the support of 10 of the 12 Senate crossbenchers.

Senator Birmingham last week travelled to Tasmania to lobby independent senator Jacqui Lambie, who usually votes against the government.

The Nick Xenophon Team (NXT) voted with the government in the House of Representatives and would be expected to support the government in the Senate.

NXT MP Rebecca Sharkie said the government's changes go "a long way" to creating a truly needs-based funding model as envisaged by the Gonski review.

She said Labor was misleading parents by claiming $22 billion was being cut from schools and that it was hard to understand why the Catholic sector was complaining when its funding was rising.

But she said the bill had weaknesses, including its slow timeframe and the fact state governments would be compelled only to maintain, rather than grow, their spending on schools.

Education Department officials last week confirmed that the six-year funding agreements struck between Labor and the states in 2013 are not legally binding and can be terminated at any time.

Senator Birmingham said the government would terminate the deals regardless of whether the Senate supports his changes.