Some history. Until around 1991 Australian telecommunications was provided by a single government owned business - Telecom (formerly Post Master General, then later Telstra). Telstra practically owned all the in ground infrastructure including the last mile copper to practically every phone in the country. Any hint of competition was crushed with obstruction, anti-competitive wholesale practices etc. Other players came in and grew some of their own infrastructure, extra long haul fibre mostly, but still practically any Telco wanting to provide services to a customer had to lease a Telstra tail line, generally at prices that made it impossible to offer anything cheaper than Telstra offered. During this period technology that the US long forget (such as ISDN) was as premium as you could get here, and technology like DSL was limited by being only possible where Telstra decided to offer it or where Telstra were forced to provide space in exchanges.
The old copper network crippled any sort of improvement to Australian internet technology - the copper lines were Telstra's cash cow and doing anything modern with them would also mean they would have to share it with the competition, so nothing much changed.
Then a previous conservative government came up with the idea of doing a "National Broadband Network" initiative. It was basically WiMax everywhere, except new places that might get some fibre over time - most likely FTTN (fibre to the node). The problem was to do anything more required buying the copper back from Telstra, and the conservatives screwed the pooch on that because they sold off Telstra as one entity - retail, wholesale and the copper network. As a new deregulated entity with some more gung ho leadership, Telstra were even more anti-competitive and not willing to give up their network. The conservatives also naively believe the free market will bring in the new technology, despite 20 years of proof that Telstra won't let that happen.
When the government they got voted out, the new more socialist government (read that as centre left) plan for the NBN was researched, and the proposal was Fibre to the Premises (FTTP). To do this they gave Telstra the option of selling its copper/access for $11B, or having it bought by compulsory acquisition (a constitutional right of the government) and a long legal fight. A deal was reached (most likely because Telstra delayed long enough and now had a new 4G network that was now its prime market) and the copper was sold, allowing the NBN project to kick off and start rolling out fibre across the country. The basic plan is the NBN Company (NBNCo) build a national fibre network and run it, and service providers sell services on it to customers.
As is natural of opposition government, they say no to everything, and think their way is better. The argument boils down to this:
a). Spend $36B and provide 96% of the population with 100M or 1GB internet over fibre. Most of that cost is covered by selling investment bonds and the eventual income from providing services on this network, so the cost is not necessarily on the taxpayer as much as the opposition would like to go on. Obvious benefit, its long term scalable infrastructure, but is more costly and slower to deploy. This is the socialist (Labour Party) plan.
b) Spend $28B and provide most of the population with 24MB VDSL using FTTN, leaving the copper as the last mile to the premises. Similar business plan, just slightly less cost. Benefit is it is slightly cheaper, and meets current internet needs. This is the conservative (Liberal Party) plan.
So - Murdoch is quite definitely a friend of the Liberals (ironic naming for conservatives), and is using his weight in the media to lay into the NBN plan every chance he gets to attack Labour. Any minor delay, problem, cost increase or simply propaganda he can find to rubbish the Labour government using the NBN is headlines. Also because if the Liberals get their way they will basically stop rolling out the current NBN and go to the lower specification one, just on the basis of slightly cheaper cost at the expense of building actual real infrastructure for the country - and that would be ideal for Murdoch too.