While Liverpool city councillors are closing libraries and swimming pools, voters are asking who will fight the coalition?

In Woolton's 19th-century public library, the reality of Ed Miliband's controversial position on spending cuts came into jarring focus.

On Wednesday, Labour-controlled Liverpool city council decided to close the library, which sits within the safe Labour constituency of Garston and Halewood. Because the leadership will not promise to reverse this or any other cut, the party, it seemed to supporters in the Merseyside heartlands, risks becoming part of the problem.

It certainly felt so for Gordon Ross, a retired university scientist who was researching local history when news of the closure came through.

"It looks as though the country is faced with a terrible dilemma," he said. "It is unfair to the voting public that the parties are all saying the same thing. There has to be an argument about the policy.,

"If the worst comes to the worst, the people in the UK will take to the streets and say 'this is ridiculous'." He even talked of a British version of the Arab spring.

Miliband had started the week trying to recast Labour as "fiscally credible" by saying that coalition spending cuts will stay and public sector pay remain frozen to try to preserve jobs, provoking an eruption from the trade unions. The general secretary of Unite, Len McCluskey, said it would leave half the country disenfranchised. The GMB's general secretary, Paul Kenny, said his union would reconsider its Labour affiliation and his Unison counterpart, Dave Prentis, accused Miliband of "breathtaking naivity". Mark Serwotka, leader of PCS, the civil service union, suggested Labour would lose the next election.

In Liverpool, party supporters found themselves at best wrongfooted, at worst undermined by Miliband and the shadow chancellor Ed Balls's position on cuts.

To the north, in Labour's safest parliamentary seat – inner-city Liverpool Walton where Steve Rotheram polled 72% in 2010 — Ben Konkwo admitted he felt somewhat betrayed. Surrounded by bits of computer at his IT repair business in a community business centre, the businessman explained where he saw the root of the problem.

"I don't think Miliband has enough experience to identify with the people," said Konkwo, who came from Nigeria and has spent more than half of his life in the UK. "If Labour is saying it will continue with the same policies [as the coalition], why would you vote for them?

"Labour has always been for the masses and the trade unions; when I heard I was very disappointed. Labour should be saying how they will make things better for people, not to continue the same cuts."

Next door, Michelle Wyatt, an accountant, was preparing year-end accounts for her small business clients – taxi drivers, builders, cafe owners. Many have been engulfed by the economic situation and public sector austerity. In a parallel universe, accountants in the City of London are going through the books in preparation for bankers' bonus season. Labour's lack of aggression towards the bankers is a running sore here."It has been like a counselling service in here because we hear everyone's financial problems," she said. "When you hear about more cuts it is disheartening because you know people are going to struggle more. People just won't vote because there is no difference. I thought Miliband was all right until I heard he was changing his policy on the cuts."

Angela Hockenhull, the manager of Walton Cornerstone, the community enterprise centre where Wyatt and Konkwo's businesses are based, said Miliband was being honest to say the cuts would not be reversed.

"I am a Labour voter, but I do question how you could go back on these cuts," she said. "If Labour took power tomorrow and tried to reverse the cuts they would have to magic the money from somewhere. I would rather this than they lied. I also look at Europe and think, please don't let that be us, and I feel this [the cuts] is a way we can stop that."

Liverpool has been hit hard by public sector cuts. Whitehall provides four-fifth's of the city council's money and that has been cut by 30%, said the council leader, Joe Anderson. It cut £91m last year and has to lose £50m this year. On Wednesday night it agreed £16m of those cuts – closing three libraries, including Woolton, a swimming pool, axing school uniform allowances and cutting funds to the children's mental health team, among others.

"It is getting absolutely desperate," said Anderson. His office is adorned with pictures of Liverpool in happier times: fireworks over the Anglican cathedral; a light show over skyscrapers built during the boom.

Anderson said Miliband's statement about keeping the coalition cuts was "no seismic shift" and criticised the union attacks, but the politics of not reversing cuts are clearly uncomfortable – not least because Anderson is a trade unionist and social worker.

"The Labour leadership is not tackling the big issues that ordinary people want handling: the way that banks have got away with this," he said. "The national party needs to do more to show that those that have benefited will pay the heaviest price. People are frustrated with Labour because they are not articulating that strongly enough."

The union critics, though, are misguided, he said. "They need to understand the plight we are in."

Derek Hatton, the former deputy leader of Liverpool council in the 1980s, said Miliband's move was an inevitable part of a political landscape that has become "various shades of grey".

"The reality is that once Neil Kinnock took the line he did in the 1980s [suspending the Liverpool party because it harboured the Militant tendency] the party would never be the same," he said. "It is correct to say that many are now disenfranchised and they will probably never have anyone to vote for because there is no room for another left party. But I am surprised that the union leaders are surprised by Miliband. That is either a game or naivety."

At the other end of his career, Jake Morrison, 19, became the youngest city councillor in Liverpool's history when he stole a seat from Mike Storey, then Liberal Democrat council leader. Morrison, a hospital worker, still lives with his mother, but is fast realising the nuanced position needed by any ambitious, modern Labour politician. He was pleased Miliband was being straight with voters, but critical too.

"Miliband is not saying clearly enough we are against what the government are doing at the moment," he said.

Morrison has sympathy with the union criticism, but stressed that the unions have a different job from the party – which is to look after their members' interests, not those of the electorate.

"As a union rep at the Royal Liverpool Hospital, I have to stand up for my members as best I can," he said. "It is a sad time to be a Labour politician and an NHS worker."

Back in Walton, at Byrne's Chippy, Janice, a single mother of three, was buying a chip cone for her son's lunch. Unemployed for five years, she missed a recent appointment about finding a job which means her fortnightly benefits have been cut to £148 plus rent. She felt the local area needed more police "to stop the kids smashing everything".

"This a big change for Labour," she said. "Labour should be promising to help people like me more. What I really want is for there to be jobs on offer. If there was another party who would offer more for single parents, I would consider them, but there's not much choice."

• This article was amended on 25 January 2012 to make clear that Woolton sits within the constituency of Garston and Halewood.