The President, Mrs McAleese, is expected to sign the Bill paving the way for the end of the dual mandate today.
The Mayo Fine Gael TD, Mr Michael Ring, has expressed doubts about its constitutionality.
However sources within all the political parties were last night confident that she will not be seeking a meeting of the Council of State to ask its advice on referring it to the Supreme Court.
The President leaves today for an official visit to Poland and the Slovak Republic.
It is understood that she has been anxious to sign the Bill personally rather than leave it to the presidential commission to do so in her absence.
Under the Local Government Bill, members of the Oireachtas will no longer be able to hold local authority seats.
While the measure, introduced by the Minister for the Environment, Mr Cullen, has attracted strong support among the political parties, some deputies and senators are opposed to it.
Its most trenchant critic, Mr Ring, who has reiterated his intention to challenge its constitutionality in the courts.
He told The Irish Times yesterday: "I have a legal team in place.
"If the President does not refer it to the Supreme Court, I will challenge its constitutionality in the High Court," the Mayo TD declared.
Mr Ring shares the same constituency as the Fine Gael leader, Mr Enda Kenny.
The party has delayed replacing members of the Oireachtas on local authorities pending Mr Ring's threatened constitutional challenge to the measure.
However, the other parties, most notably Labour, have been holding conventions to replace their deputies and senators.
This is intended to give the new councillors a period to build an electoral base in advance of the local elections in the summer of next year.
Mr Cullen is expected to make an order putting a deadline of September or October for members of the Oireachtas to stand down as members of local authorities and qualify for the financial "sweetener" he has introduced.
This is a total of €12,800, including the statutory entitlement of €7,800 for retiring councillors and a further €5,000.
An analysis by the General Council of County Councils after last year's general election, showed a surge in the number of TDs who also held local authority positions.
A total of 101 of the 166 members of the 29th Dáil also held seats in county councils and urban and borough councils, the survey revealed.
This was a rise of 22 on the 79 dual-mandate holders in the outgoing Dáil.
