Unite put a lot of effort into the general election campaign. In practical terms, it was valuable, for example in helping to push back the BNP in Barking.
But it was accompanied by no effort at all to push a distinctive political message, even on issues where Unite has clear union policy. Mailings to Unite members appealed to them to vote Labour on such grounds as trusting in the "experience" of the government as against the untried Tories.
On 11 May Unite joint general secretaries Tony Woodley and Derek Simpson put out a statement supporting a Labour/ Lib Dem coalition. If that had come off - and it now looks as if it was never really on the cards - it would have meant giving the New Labour right wing a huge counterweight to union and working-class demands in the shape of Lib Dem coalition partners whose policies include new legislation to allow the government to ban strikes in public services.
Unison was more dignified, implicitly criticising the coalition talks, saying that the election result did not mean a popular mandate for cuts, and promising that the union will organise to fight those cuts.
The record of the Unison leadership, however, makes that promise untrustworthy - unless left-wing challenger Paul Holmes can oust sitting general secretary Dave Prentis in the current Unison leadership election.
GMB supported Labour in the election campaign, but quietly, except in support for the anti-fascist campaign Hope Not Hate. It has made no statement since 6 May.
The post and telecom union CWU was also quiet, putting out an edition of its union newspaper in early May which said... nothing about the election. It has made no comment since 6 May, though the Tory/ Lib Dem government is sure to go for privatising Royal Mail.
The rail union RMT contributed actively to winning re-election for left Labour MP John McDonnell, but said almost nothing about the election on its website.
The lecturers' union UCU has already felt the sharp edge of cuts in further and higher education, and struck in several London colleges on 5 May. But its general secretary Sally Hunt responded to the election like this: "The new government has a unique opportunity to build a national consensus that puts education at the heart of our recovery".
As well say that the election of Joseph Ratzinger as Pope Benedict XVI gave the new pontiff a unique chance to promote atheism, if he should wish to. Hunt justified her optimism by claiming that the "public expects Lib Dems to deliver" on their policy to abolish university tuition fees.
The civil service workers' union PCS put out a statement on 7 May which quoted general secretary Mark Serwotka presenting his chief concern after the election as... pushing for proportional representation! As if Nick Clegg needed more boosting...
Presumably drafted or approved by the Socialist Party, which has a controlling influence in PCS, the statement claimed, surreally, that the "outcome [of the election] shows the public have rejected the main Westminster parties".
Unison had commented, accurately, that the 6 May result could not be taken as showing any popular mandate for cuts. PCS "improved" that comment into the idiotic claim: "Election result is a rejection of cuts agenda".
It went on, fatuously, to propose as the PCS alternative to cuts... stricter tax collection.
"The public have rejected the main parties"? The three biggest parties got 88.1% of the vote. That share was down 1.4% on 2005. UKIP and the BNP increased their share by 2.1% (mostly by standing more candidates than in 2005).
Votes for parties that could even arguably be reckoned to the left of the three biggest parties went down, not up.
TUSC, the electoral front run by the SP (with some participation from SWP), got 0.04% of the vote.
For socialists to use elections as a sounding-board even when they can win only a small vote may make sense. For them to claim that their 0.04% of the vote shows that the public has rallied to them and rejected the parties that got 88.1% of the vote is stupid.
Evidently the big majority of working-class people who want a fight against cuts voted Labour. That will not have been because they trusted Gordon Brown and Alistair Darling to stop cuts - they are not stupid - but because they thought they would have more leverage against cuts with a Labour government than with a Tory or Tory-led government.
Activists in the unions need to organise now to use that potential for leverage which comes from Labour's links with the unions. More: we need to organise to make the anti-cuts majority shown by opinion polls into an effective industrial and political force.
The unions should map out a programme of agitation, rallies, demonstrations, and escalating industrial action now, rather than "waiting and seeing". And they should intervene to reclaim a working-class voice in the Labour Party, and to turn the Labour Party - or at least sections of it - into a political force for the anti-cuts fight.