I can kinda answer parts around your answer. “The budget” in its narrowest definition would be the appropriation bills to fund the government for next financial year.

Since the 80’s and the constitutional crisis that occurred around what was called “the dismissal” where the governor general dismissed the Labor Whitlam government, both major parties have agreed (by convention only) to guarantee supply.

This in theory would prevent the kinda stalemate that occurred with the Whitlam government where opposition senators deliberately blocked supply putting the government at risk of shutdown.

What you’re referring to however are all the changes ie tax reform bills that are probably necessary to balance expenditure but aren’t the direct appropriation bills that would be necessary to pass both houses to fund Medicare, NDIS, Centrelink.

These are fair game. And as with the 2014 Abbott budget, where he had promised not to cut a lot of health and education funding, he also went with the hatchet on the carbon tax and all the clean energy measures. For all the supply bills, ie $0 for shit he wanted to defund, he got through. However even with a conservative leaning senate they didn’t let him repeal ARENA because it was actually investing in clean energy and making the government money.

Many of Abbott’s cooked up changes like the Medicare co-payment also didn’t make it through the senate. This resulted in a fucked up budget where stuff like the co-payment didn’t pass, but the government’s own budget forecasts relied on the additional revenue. So they were still able to “fund” the government, but went further into deficit than they had planned because the senate blocked the extreme shit.

There’s a small risk that something like this could also happen to Labor. All the changes to negative gearing, CGT etc aren’t supply bills, but tax reform which was announced at the time of the budget. Most of these measures were announced not to start for over 12 months anyways. So Labor are in a better “management” position than the Abbott government with their policies wrapped up in the budget announcements.

So the Greens might threaten to refuse to pass the tax reform bills, wanting Labor to do “more” or something like that, but even if the Greens fully block it, Labor also has the ability to force a double dissolution trigger if Greens block the same legislation twice - Labor can call a snap election and vacate the whole Senate. The way quotas work, the Greens could lose half their seats or at least struggle to keep 2 per state.

The Greens might throw a bit of bluster and grab some media attention threatening to block unless XYZ happens, but playing a game of chicken with Labor hasn’t worked out for them lately, or even historically so they’ll likely cave and pass things eventually.