After the Senate sent his higher education bill packing, Education Minister Christopher Pyne dropped into a Universities Australia reception, which serendipitously happened to be in full swing at Parliament House while the vote was on.

Addressing the academic crowd, Pyne invoked Churchill’s fighting words about this not being the end, just the end of the beginning.

On Wednesday Pyne’ll introduce a revised version of his legislation into the lower house, incorporating the amendments proposed by crossbenchers. Next year, the Senate will be voting on the bill again.

Pyne lobbied so frenetically to try to pull off a victory on Tuesday that Palmer United Party senator Glenn Lazarus issued a statement accusing him of harassment by texting. The government desperately wanted a win to take something positive out of a final sitting fortnight that is miserable, regardless of the pep talks Tony Abbott keeps giving about what a year of achievement it’s been.

Pyne had the support of Universities Australia but the required six crossbenchers could not be mustered.

There was not much trouble with Liberal Democrat David Leyonhjelm and Family First’s Bob Day.

Getting the Motoring Enthusiast Party’s Ricky Muir was something. He is notionally an ally of the Palmer United Party, which was against the changes. But he voted with the government, despite a public warning from ex-PUP senator Jacqui Lambie that he could eventually face trouble, if the package were implemented, with the cost of educating his large family.

Independent John Madigan also voted for the second reading – the point at which the bill was defeated.

But PUP’s two senators (the other is Dio Wang) voted against, despite people parsing Clive Palmer’s Monday words on the issue and wondering if there could be a change.

Lambie was adamantly opposed, even apart from the fact she’s against everything from the government at the moment because of her row with it about defence pay. It’s interesting that Lambie was in sympathy with PUP despite her formal split from the party but Muir was not, although he has an alliance.

The other no vote was from South Australian independent Nick Xenophon, who didn’t want the matter to be dealt with this year.

Of these four “no” voting senators, the government would have to win over two of them, assuming it keeps on side Madigan, who is reserving his position on the bill itself, as distinct from the second reading stage. Can it do so?

Predicting PUP and Lambie is impossible; Xenophon comes from a state that has been hit by various other measures; Madigan could drift away.

The government is helped by the support of Universities Australia, although that body wants further changes. But it does not have public backing. Tuesday’s Essential poll found more than half (56%) said the Senate shouldn’t agree to the legislation while fewer than a quarter (23%) said it should.

The university package, with its fee deregulation and reduction in government subsidies for students, is one of the more spectacular ways in which the Coalition misled the voters before the election. All its pre-election messages were that it was not planning major upheavals.

Abbott told a Universities Australia conference in 2013: “In an era of busy government and constant change, it’s insufficiently recognised how often masterly inactivity can be the best contribution that government can make to a particular sector. A period of relative policy stability in which changes already made can be digested and adjusted to (such as the move to demand-driven funding) is probably what our universities most need now.”

The question of timing will be important in the battle. The longer the legislation is strung out in the Senate the second time around, potentially the more difficult it could become for the government. The changes are supposed to start in 2016. If it got to a point where there was pressure for the start date to become 2017, that would be after the next election.

Education is the ALP’s natural ground. Given public opinion, the deregulation issue is a strong one for Labor, but it is stronger if the legislation is not passed. If it is through and the new arrangements have commenced, a Labor promise to unscramble the egg would run into all sorts of complexities.

The stakes are high for both sides of politics, let alone for universities and future students. Lazarus had probably better get used to being harassed. It could get a lot worse.