David Cameron faces one of the major battles of the coalition this summer when George Osborne outlines spending plans for the 2015-16 and is facing private warnings that if he does not have a good budget in two weeks time, he could face a leadership challenge. A group of cabinet members, dubbed the National Union of Ministers after the militant National Union of Mineworkers, are resisting further cuts to their departments. They are targeting the protected welfare, education and international development budgets whose ministers are now being dubbed the Union of Democratic Ministers after the moderate UDM trade union.

'The mine owners'

David Cameron & George Osborne

The prime minister and chancellor know they are boxed in because health and international development spending are guaranteed and the Lib Dems are digging in their heels on welfare. They know they face a bruising spending round.

Nick Clegg & Danny Alexander

The Liberal Democrats accept that an extra £10bn in cuts will have to be found for 2015-16. They have a simple challenge for the Tory NUM ministers demanding cuts in welfare: why not look at benefits paid to millionaire pensioners?

National Union of Ministers (NUM)

Named after the militant National Union of Mineworkers, whose leader Arthur Scargill led a year-long strike in the 1980s

Theresa May, home secretary

As the most senior member of the cabinet agitating against further cuts to her department, the home secretary is the shop steward of the union. May has a simple view: she has taken some difficult political decisions to deliver cuts in this parliament, such as changing police pension rights, and it is time for welfare to take its share of the burden.

Leadership ambition: 9 out of 10

Philip Hammond, defence secretary

The defence secretary is an unlikely militant. Before the election he was shadow chief secretary to the treasury and had assumed, until the formation of the coalition, that he would enforce cuts. But Hammond is fighting hard against further reductions in his budget because he says military chiefs signed up to record cuts in 2010 on the basis that spending would rise again in the next parliament. His intervention over the weekend was mainly aimed at the Liberal Democrats who, in his eyes, are wrongly blocking further welfare cuts.

Leadership ambition: 6 out of 10

Vince Cable, business secretary

The business secretary joked that he is on the NUM's shop steward's committee. Cable is on common ground with May and Hammond in believing that his department has suffered enough cuts. He believes that any further cuts would jeopardise a series of initiatives to promote economic growth. But Cable disagrees with Hammond and May on welfare – he believes this has been cut far enough and the Trident nuclear deterrent should be offered up first.

Leadership ambition: 7 out of 10. Reduced now that Nick Clegg's position is strenghthened after Eastleigh byelection victory.

Chris Grayling, justice secretary

A junior and recent recruit to the NUM, Grayling is "muscling in" according to one Whitehall source. But he believes that his department has endured strong cuts in this parliament. He is involved in something of a battle with the treasury over his plans to reduce reoffending rates by introducing a payment by results system for voluntary groups and private companies taking over the probation service's work.

Leadership ambition: 3 out of 10

Possible NUM member

Eric Pickles, communities secretary

The Thatcherite communities secretary is a reluctant militant because he is a strong believer in trimming public spending. But he may be tempted to side with the NUM because he shares the belief that welfare needs to be targeted before his budget suffers further cuts.

Leadership ambition: 1 out of 10

Union of Democratic Ministers (UDM)

Named after the Nottinghamshire-based Union of Democratic Mineworkers who rejected the militant tactics of the NUM

Jeremy Hunt, health secretary

The health secretary is the most senior and confident member of the conciliatory UDM group of ministers whose budgets are currently "ringfenced" – protected from major cuts. The most important commitment David Cameron made before the election was to guarantee that NHS spending would rise in line with inflation. This will apply during the next spending period covering 2015-16.

Leadership ambition: 6 out of 10. Hunt knows his ambitions suffered a major blow when he was deemed to have been overly soft as culture secretary on News Corp.

Justine Greening, international development secretary

The international development secretary is in a curious position. Her budget is guaranteed because the prime minister has pledged to meet the UN target of spending 0.7% of Gross National Income (GNI) on overseas aid by the end of this year. But Greening believes that further efficiencies could be introduced and probably would not shed a tear if the axe fell.

Leadership ambition: 6 out of 10

Michael Gove, education secretary

The education secretary may find he has to switch camps and embark on the startling step of joining the NUM. There is mounting speculation that his schools budget could be targeted in the 2015-16 spending round because George Osborne will have so little room for manoeuvre elsewhere. The schools budget has a "flat cash" guarantee until 2015 – it will rise and fall in line with inflation. But it is currently rising slightly below the rate inflation because it is relatively high.

Leadership ambition: 7 out of 10. Denies any interest but is struggling to convince people he really believes that

Iain Duncan Smith, work and pensions secretary

The work and pensions secretary is sitting out the NUM debates. He offered up £10bn of cuts in last year's spending review but saw this trimmed to £3.6bn after the Liberal Democrats vetoed his ideas to remove housing benefit from the under-25s and to cap child-related benefits for families at two children. Duncan Smith would he happy to place these on the table again, just as he would be happy to save billions by cutting universal benefits to pensioners such as the winter fuel allowance.

Leadership ambition: 0 out of 10. Been there, done that