Finance: As he enters the Department of Finance in Merrion Street, Mr Cowen will find himself pulled in two opposite directions. His senior officials - and perhaps his instincts - will tell him to keep a tightish rein on spending and let the economic lift improve the public's mood.
However some of his cabinet colleagues and his party grassroots will be looking on the new man to win round the electorate by spending more on key areas of health, education and welfare.
The economic recovery has boosted the Exchequer finances and the expectations facing Mr Cowen are significant. The headlines have been dominated by reports of rising growth and buoyant Exchequer finances. The Taoiseach has nodded to the need for a " socially caring strategy". With the next election starting to come into sight, the pressure will come on the new Minister from every angle.
He will not have much time to draw breath. The so-called "estimates season", when the Department of Finance negotiates with other Departments, is already well under way.
Key decisions will have to be made in the coming weeks about the level of spending next year and where it will be allocated.
The first key question facing Mr Cowen - and his Cabinet colleagues - is whether to let spending growth accelerate in the run up to the next election. Spending was let rip before the last election, necessitating politically-damaging cutbacks in some areas after the last election. Subsequently, spending has been brought back under tight control, with new control mechanisms putting the Department of Finance in the ascendant.
The Exchequer finances may be in good shape, but Mr Cowen's wriggle room in framing his spending plans may be limited enough, particularly given the pressures for more resources in many areas.
If the Government sticks to a commitment in the Sustaining Progress agreement, then current spending growth must be held to the level at which the economy is growing, which is expected to be around 8 per cent next year (this is nominal growth before adjustment for inflation).
Much of this money will almost allocate itself. The Department of Finance estimates that in this year's Budget - allowing for inflation - spending on services would have to rise by around 3 per cent to maintain current service levels. Subsequent public pay increases and other spending commitments have probably increased this to around 4 per cent.
The Minister might thus have the same again - about 4 per cent or close to €1.5 billion - to allocate on real increases.
He will have no shortage of applicants, starting with the new Ministers for Health, Education and Social and Family Affairs. Mr Cowen has a reputation as a Minister not afraid to say "no".
However, he will realise that the amount of money at his disposal is enough to put a bit of a gloss on Budget day, but not to embark on a new spending spree.
Looking at investment spending, the last Budget set the groundwork, outlining a multi-annual programme for capital investment.
Almost €35 billion is due to be spent over the years 2004-2008 on projects in areas such as transport, education and health. Again, not too much room for manoeuvre for the new Minister.
If the Government sticks to the existing tracks on which policy is moving, the next Budget does not quite write itself, but would be fairly predictable. It would involve:
It would not quite be a "feelgood" Budget, but it would allow the Government to try to put on a more caring face and avoid the kind of decisions which have annoyed voters in recent years.
Or should we expect a more fundamental change of approach? Yesterday Mr David Begg, the ICTU general secretary, called on the new Cabinet to adopt "a more progressive agenda".
The new Minister for Finance should introduce a "generous, enlightened and socially-focused budget". Meanwhile, the new Minister for Foreign Affairs, Mr Dermot Ahern, was on RTÉ radio talking about a change of " emphasis".
Progressive Democrat Ministers - and some from Fianna Fáil - have emphasised in recent weeks that there would be no fundamental change of direction. However, with borrowing and debt low, there will be an inevitable temptation to quietly shelve commitments to restrain spending growth. Interestingly, the Tánaiste, as Minister for Health, may on the one hand be looking for more funds, while on the other calling for the Government as a whole to maintain restraint.
The new Minister is likely to come into office preaching the need to keep the finances in check and to ensure value for money through reforms. Whether this rhetoric is matched by action or whether the temptation to spend a bit more wins out will become clear when the spending plans for next year are outlined in November as the first part of the 2005 Budget.
Cowen's inheritance: key 2004 indicators
GNP growth (Dept of Finance forecast) 4.2%
Inflation rate (August) 2.6%
Unemployment rate (August) 4.3%
Exchequer borrowing (Dept of Finance forecast) €1.8 billion
Debt to GDP ratio (Dept of Finance forecast) 31.5%