Fine Gael said last night that the gloves were off in its opposition to the Fianna Fáil/PD coalition now the Nice Treaty had been passed.
The party pledged to begin in earnest a campaign to "rout this treacherous Government" and to "cut out the gangrene of corruption in politics".
The Labour Party also said the Yes vote was not an endorsement of Government policies and that there was real anger at the dishonest and deceitful election.
Fine Gael leader, Mr Kenny, said, for the sake of the country, it held its fire before the referendum.
"The ratification of the Nice Treaty has freed up Fine Gael to pursue its primary political object: to remove the current Government from office," he said, adding that his party would now fulfil its "political and moral imperative" to restore public confidence in government and its institutions.
"Fine Gael now finds itself in the highly unusual position of being probably the sole Opposition in modern democracy, facing a Government that bought its election," he said.
He warned that the country was in dire financial straits.
"A decline in public monies automatically means a decline in the quality and quantum of our public services. Therefore it is the people who will pay for the Government's disastrous management of the public finances, especially those who can least afford it, the sick and the disadvantaged."
According to Mr Kenny, Fine Gael was in transition and it would take time and effort to build the party as a "powerful political movement".
"It is still early days in that process but we are confident for the future. I want to assure the disillusioned electorate of my intention to lead a credible alternative government."
Mr Kenny welcomed the Yes vote and said it would strengthen Ireland's position in an enlarged EU. He called for MEPs to be given the right to speak in the Dáil and Senate on European matters, and said the Forum on Europe should be maintained.
The Labour leader, Mr Quinn, said Government would be foolish to regard the vote as an endorsement. "There is real anger out there at the dishonest and deceitful general election campaign and this will be apparent when the next elections are held. This was a different kind of Yes because the question and the context in which it was put was changed since last year. This is largely due to the concessions won by the Labour Party since the last referendum."
He said he was delighted with the referendum outcome.