The TUC's annual gathering backed a motion which included calls to build "a broad solidarity alliance of unions and communities under threat".
TUC chief Brendan Barber warned that big cuts would make Britain a "dark, brutish and more frightening place".
The PM's spokesman said they wanted "partnership" with the unions to tackle the deficit.
The opening of the TUC's 142nd congress - the first under a non-Labour government since 1996 - comes amid concern among unions about the speed and scope of the coalition's programme to reduce the £155bn deficit.
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Most Whitehall departments have been ordered to plan for savings of between 25% and 40% ahead of the comprehensive spending review of 20 October.
Delegates debated a motion calling for the TUC's general council to "support and co-ordinate campaigning and joint union industrial action, nationally and locally, in opposition to attacks on jobs, pensions, pay or public services".
It could lead to different unions calling strikes on the same days if the cuts are not scaled back, although BBC Political Editor Nick Robinson said trade union laws and union leaders' desire to build a wide coalition against the cuts made a "winter of discontent" unlikely.
The motion rejected the idea that cuts were necessary to pay for the deficit and said they were a "savage and opportunistic attack on public services" which "goes far further than even the dark days of Thatcher".
TUC general secretary Mr Barber told delegates: "These are not temporary cuts, but a permanent rollback of public services and the welfare state. Not so much an economic necessity as a political project driven by an ideological clamour for a minimal state.
"What they take apart now could take generations to rebuild. Decent public services are the glue that holds a civilised society together and we diminish them at our peril. Cut services, put jobs in peril and increase inequality, that's the way to make Britain a darker, brutish, more frightening place."
He said no-one took industrial action lightly, but added: "Where members, faced with attacks on jobs, pay or pensions take a democratic decision for industrial action, they will have the support of unions and the TUC stands ready to co-ordinate that."
BBC business reporter Simon Jack said no dates had been named for industrial action - but the motion meant unions were "standing ready" to do so if necessary, although there was no detail of what form it could take. He said the first co-ordinated action was not likely to take place until February or March 2011.
By Ben WrightPolitical correspondent, BBC News
Ministers have spent the summer softening the public up for cuts but, with big job losses looming, the unions haven't been persuaded.
Brendan Barber called the government's assertions "insulting claptrap".
Some trade union leaders, such as Bob Crow and Mark Serwotka, predict civil disobedience and coordinated strike action in response to cuts. But moderates like Mr Barber want to temper the tone and place the union movement at the centre of an alliance with the public, charities and community groups who oppose the cuts.
So talk of a new winter of discontent may be wide of the mark, not least because secondary picketing is now illegal. But also because union leaders like Barber will be very wary about embarking on strike action that hits the users of public services hard and risks turning their members into villains.
The government wants to sound moderate too, hence Francis Maude's insistence he wants to see engagement and "partnership" between the unions and ministers. But confrontation looks likely so long as there's a chasm between the Treasury and the unions on how to deal with the deficit.
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Only one delegate spoke against the motion, Jim McAuslan, general secretary of the airline pilots' union BALPA. He said it might be seen as an "open goal" for the government, and warned some union colleagues were "getting the tone wrong" in resisting every cut and they had to get the message out beyond unions to the wider community.
Rail, Maritime and Transport Workers' (RMT) leader Bob Crow has called for a campaign of "civil disobedience" but Mr Barber told the BBC he thought that was "counter-productive".
Instead he said he favoured "a broad-based campaign... to look to harness public opinion behind the case for a different approach to managing our economy."
He spoke against a purely critical campaign, asking unions to promote an "alternative to austerity that encourages growth and jobs".
Cabinet Office Minister Francis Maude told the BBC: "We will listen very carefully to what they [the unions] say and the arguments that they make, there's no question about that. We are not going back to the days where there's a complete stand-off between the trade unions and the government. Those days are gone."
But he said the coalition government had "inherited a terrible budget deficit" and was having to borrow £1 out of every £4 "just to keep the lights on".
He said it was "absolutely necessary" to eradicate the budget deficit - to stop interest rates going up and "choking off" the recovery.
He said the government wanted to protect front-line services and jobs and had spent months renegotiating with the government's suppliers to cut costs, to try to protect as many jobs as possible.
Downing Street also said the government wanted "a genuine partnership with the trade unions".
The PM's spokesman said. "We need to deal with the deficit, we want to work with everyone in tackling that."
For all the rhetoric of the union leaders, the BBC's Political Editor Nick Robinson said it would be up to individual members whether to take strike action in ballots over the coming months.
But he said there were growing indications of disquiet among council workers and police officers.
Dave Prentis, general secretary of the Unison public services union, is calling for united action to defeat the government's "austerity agenda".
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Unite, the UK's biggest union, says it wants a "robust campaign" to protect public services, while the GMB argues that three-quarters of a million jobs could be at risk.
The RMT accuses ministers of launching "all-out class warfare".
The government is not sending a minister to address the congress but Business Secretary Vince Cable has said he will be willing to speak to representatives to discuss their concerns.
Acting Labour leader Harriet Harman addressed the TUC while the five candidates to become leader made their pitches to union delegates in the final hustings of the campaign.
Each stressed their solidarity with the trade unions in the face of the anticipated spending squeeze but David Miliband said critics of the cuts needed to win the political arguments while brother Ed Miliband called for a "responsible approach" to opposition.
The TUC congress is the curtain-raiser for the party conference season and will be followed over the next three weeks by events held by the Lib Dems, Labour and the Conservatives.
Union delegates have backed joint industrial action if "attacks" on jobs, pensions and public services go ahead.