Fine Gael is doing well especially, but so also are Labour and Sinn Fein.
Mr Kenny's centre-right Fine Gael won 76 seats and Labour 37 in the 166-member parliament.
Richard Bruton, finance spokesman for the opposition Fine Gael party, called the budget "jobless and joyless".
Labour leader Eamon Gilmore appealed to voters not to give Fine Gael a "monopoly of power".
Some lawmakers from the main coalition party Fine Gael are likely to vote against the bill, however.
Fianna Fail and Fine Gael emerged following a split in nationalist opinion over the 1921 Anglo-Irish Treaty.
Fianna Fail was once seen as more centrist, Fine Gael as more conservative, but differences have blurred.
The Fine Gael-Labour coalition said it would bring in legislation and regulation on the issue by the summer.
Other past contests have seen General Sean Mac Eoin stand for Fine Gael.
Among opposition parties only Fine Gael, which gained 20 seats to recover much ground lost in 2002, could be satisfied.
At the end of the third count on Saturday, Sinn Fein's Martin McGuinness and Gay Mitchell of Fine Gael, were both excluded.
Meanwhile from the Irish parliament, Fine Gael MP and Energy Spokesman Simon Coveney said Europe should develop an "offshore supergrid", harnessing wind energy.
Despite his party's bleak look-out, Fianna Fail's Micheal Martin kept up his message that Fine Gael's election manifesto was neither credible nor costed.
So, there has been a vacuum which the current Fine Gael-Labour coalition government says it will fill with a new law by the summer.
Local Fine Gael representative Michael Ring has asked TV3 to consider putting a new transmitter near Belmullet, County Mayo, to serve the soap's fans.
After a poor performance in the Irish General Election last February, the party was replaced by the current coalition government of Fine Gael and Labour.
One recent poll gave the rival centre-left coalition of Fine Gael and Labour, which last held office in 1997, a nine-point lead over the government.
ECONOMIST: Ireland's unpopular government: Bertie's blues | The
The main parties are Fianna Fail, who won the most seats in the last election in 2007, Fine Gael, Labour, Sinn Fein and the Green Party.
Centre-right group spokseman and Irish Fine Gael MEP Jim Higgins told MEPs that at any one time "45, 000 vehicles breach tachograph rules", leading to "more fatigued drivers".
Ireland's right-wing nationalist party, Fianna Fail, led by Bertie Ahern, won a general election, beating the moderate-conservative Fine Gael, led by the outgoing prime minister, John Bruton.
Only this week parliamentary representatives from Meath, including former premier John Bruton, head of the Fine Gael opposition party, met Trinity College officials to discuss the possible move.
His decision on Saturday to resign as Fianna Fail leader while remaining PM was met with an angry response by the opposition Fine Gael, Labour and Sinn Fein parties.
Fine Gael, with its roots among better-off farmers and businessmen, worked happily in the last parliament with Labour and the Democratic Left, which like to think they are on the left.
The pork-barrel king of Tipperary North, Michael Lowry, topped the poll as an independent although he was lately sacked as a minister, and from Fine Gael, in a cloud of sleaze.
The Irish government has been under pressure from the main opposition party Fine Gael over the effectiveness of the investigation into the car bombing of Omagh, County Tyrone on 15 August 1998.
Buoyed by polls predicting at least 70 seats for Fine Gael in the 166-seat Dail, Enda Kenny spent Thursday in counties Donegal and Sligo, before returning to his home in Castlebar, Mayo.
When Fine Gael and Labour agreed to work as coalition partners, they issued a joint document saying voters had chosen parties "to begin mending the pieces of a fractured society, a broken economy".
Fine Gael has questioned the effectiveness of new laws passed to help convict the bombers and demanded answers to reports the Irish government interfered in police investigations of the bombing for political reasons.
Within the coalition government a large group of the Fine Gael party members, the party with the most seats, have vowed to oppose any liberalizing of abortion, even if the European panel recommends it.
Earlier this year, for instance, two hackers breached and defaced the website of Irish political party Fine Gael, proclaiming it the work of Anonymous when most supporters had no idea what was going on.
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