The Turnbull government school plan cuts $1.2bn over 10 years from schools compared with regular increases in current legislation, according to a parliamentary budget office costing prepared for Senator David Leyonhjelm.

The costing has reportedly prompted Leyonhjelm, a small-government libertarian, to reconsider his opposition to the Gonski 2.0 school funding plan but could spell trouble for the government among crossbench parties who have argued for more funding for needy schools.

According to the government, Gonski 2.0 increases funding by $18bn over 10 years) compared with current levels, while Labor focuses on the fact it is a $22bn cut relative to funding promised in needs-based funding agreements with the states.

The PBO costing, prepared and released on Friday, compared the Turnbull government plan with the regular funding increases owed to schools under the Australian Education Act.

Under the act underfunded schools get 4.7% annual funding growth, schools at the resource standard get 3.6% a year, and overfunded schools get 3% a year.

The rates apply to public schools in the “participating states” with needs-based funding agreements (New South Wales, South Australia and the Australian Capital Territory) and for all non-government schools. Public schools in the other, non-participating states now get the same amount but are not guaranteed it by legislation.

The costing finds that over four years Gonski 2.0 increases school funding by $117.4m compared with current legislation.

But over 10 years, the PBO costing said, the government’s plan would reduce spending on schools by a total of $1.2bn.

It is unclear whether the PBO costing assumes that government schools in non-participating states will continue to receive the same indexation as those in NSW, SA and the ACT, or accounts for the ministerial discretion to decrease their rate of funding growth, which would change the costing outcome.

Leyonhjelm has so far said he would oppose the Turnbull government school plan because it increases funding.

“However, I must say my thinking on [Gonski 2.0] is not as hard as it was as a result of this analysis,” he reportedly told the Australian.

Leyonhjelm’s vote could be crucial because if the nine Greens senators vote to block the bill, the government will need 10 out of 12 of the remaining crossbench senators to pass it.

The Greens and the Nick Xenophon Team have demanded that the government give needier schools faster funding growth and impose conditions on states to increase their share of school funding, although NXT’s education spokeswoman, Rebekha Sharkie, has said Gonski 2.0 does implement needs-based funding – suggesting that NXT may pass it.

The Greens will determine their position in the party room next week, before a push by the government to pass the bill that week before the winter recess.

The PBO costing appears to bear out a concern expressed about the Gonski 2.0 changes by Greens education spokeswoman, Sarah Hanson-Young, who has noted it “does provide a smaller amount – a reduction – to what has been legislated”.

“I don’t think in 2017, when we are weighing up priorities of government spending, that we should be looking for savings in our education budget,” she said in May.

In response to suggestions that some schools could be better off if the Gonski 2.0 bill were blocked, the education minister, Simon Birmingham, has warned that public schools in some states and territories could face funding cuts because they do not have binding agreements locking in yearly increases.

Speaking to Guardian Australia’s politics live podcast in May, Birmingham suggested the government could revert to funding levels in last year’s budget and noted it was not bound to increase funding for all states, referring to the non-participating states Queensland, Victoria, Western Australia and Tasmania, and to the Northern Territory.