The double by-election next spring would severely test the Government's attempt to transform its image, writes Mark Brennock, Chief Political Correspondent.
By the time the Government parties face the voters of Meath and Kildare North, they hope to have planted firmly in the public mind that they are a caring Government.
A new minister for finance, almost certainly Mr Cowen, will deliver the December Budget. It is expected to give some tax relief targeted particularly at the lower paid, along with other popular measures.
Yet Governments lose by-elections, and have done so on every occasion since 1982.
A double by-election loss would be a significant psychological blow to the Coalition's recovery programme. Victory in just one would be a cause of great satisfaction for them. By-elections also have the capacity to provide an enormous morale boost to whichever Opposition party or Independent can best capture the anti-Government feeling.
These contests usually see a mini-stampede of voters to whoever is portrayed as the candidate most likely to defeat the Government, so the competition to be seen as the leading opposition challenger will be fierce.
Strategists in all parties therefore see the first constituency opinion poll as possibly the most important event of the entire campaign. If one opposition candidate can emerge as a clear challenger at an early stage, then many voters will abandon other hopefuls and rally around them.
At this early stage contenders for party nominations in both constituencies have begun to sound out support for what will be long, exhausting campaigns.
Kildare North
This three-seat constituency will become a four-seater at the next General Election, giving the winner of the by-election a good chance of retaining the seat.
Fianna Fáil came within just 135 votes of taking a second seat out of three here in 2002 when Fine Gael's Bernard Durkan held off Cllr Paul Kelly.
Mr Kelly wants to run again, but it is not yet known whether the politically interested Mr Charlie McCreevy jnr will seek to run at this point. If he doesn't, the McCreevy camp may back Cllr Michael Fitzpatrick.
The Progressive Democrats' Senator Kate Walsh won 12 per cent of the vote last time, and is important to Fianna Fáil's chances. While her vote seems too small to make her a serious contender, it is large enough to give her transfers a big influence on the outcome. Last time around 65 per cent of them went to Fine Gael and Labour.
Fine Gael has no clear front-runner at this stage. New young Kildare Cllr Katie Ridge is mentioned, as is Leixlip Town Cllr Thomas Neville, son of Mr Dan Neville TD. Other contenders may emerge.
Labour Cllr Kevin Byrne is from Mr Emmet Stagg's area, and has the best chance of securing the bulk of his vote. Should he win, however, Labour would go into the next General Election with two sitting deputies from Straffan, thus guaranteed to lose one.
Cllr Paddy McNamara topped the poll in the local elections in Naas at the other end of the constituency. He is under 40, and the high level of exposure in a by-election would make him a perfect running mate for Mr Stagg for the future as Labour seeks two seats here. Another possibility is Cllr John McGinley, a national executive member and ESB worker director.
Cllr Catherine Murphy, a former Democratic Left and Labour member who has done well in the constituency in the past, may be a contender. The Green Party's Ms Anne Kelly McCormack won 2,000 votes or 6 per cent last time out, and the party is expected to contest the by-election.
Meath
This five seat constituency will be split into two three-seaters at the next General Election, leaving whoever wins the by-election to choose between the two new constituencies before facing a difficult task to retain the seat.
The 45 per cent Fianna Fáil vote here last time was one of its best in the State, helped by the presence of a Minister, Mr Dempsey. Despite speculation, the Taoiseach will hardly demote the constituency's Minister just as he prepares for an election campaign.
Some in Fianna Fáil are already suggesting an approach to former Meath footballer Mr Colm O'Rourke, who would have strong local appeal. It is not yet known whether he would be interested. Otherwise the chairman of Meath County Council and Dempsey's right hand man, Mr Tony Reilly, may seek the nomination. Two other councillors Mr Jimmy Fay and Mr Noel Leonard are also mentioned.
Former Fine Gael TD Mr John Farrelly is a possible Fine Gael contender, as is newly-elected Cllr Charles Bobbett and Mr Shane McEntee, brother of Meath footballer Gerry McEntee. Mr Bruton's son Matthew is mentioned as a possible future contender but is still a student.
Former ICTU general secretary Mr Peter Cassells is Labour's favoured candidate, although he has initially expressed a lack of interest. Labour has not yet taken "No" for an answer and plans to put together plans for a substantial, well-organised and financed campaign in the hope that this might change his mind.
If it doesn't, former Attorney General Mr John Rogers withdrew at the last minute from the pre-2002 selection convention and might yet be interested. Barrister Peter Ward did well in 2002 as a first-time candidate, but performed poorly in the recent local elections. A 23-year-old activist from the Slane electoral area, Mr Shane Cassidy, is also mentioned as a contender with a prospect of building towards a serious Dáil challenge in the future.
Sinn Féin will make an enormous effort to get Mr Joe Reilly elected. Having come within 1,800 votes of a seat in 2002, the recent constituency revision appeared to kill off his prospects. It put his home base of Navan in one of the new constituencies, and the traditional republican vote in north Meath in the other. Mr Reilly now has a last chance to win a seat in the five-seat constituency. Success would give him two years as an incumbent to prepare to defend the seat in one of the smaller constituencies.
Former Labour deputy, now Independent councillor Mr Brian Fitzgerald is determined to run in Meath East in the next General Election, but said yesterday he has not yet decided whether to contest the by-election.
The Green Party won 2,337 votes last time with Mr Fergal O'Byrne, and will contest the by-election. The PDs, meanwhile, may run Ms Sirena Campbell, a 26-year-old social worker who was an unsuccessful local election candidate but secured close to half a quota in the Julianstown area in the local elections.