On 26 March 2009, the Presidency Council (President Jalal Talabani, Vice President Tariq al-Hashemi, Vice President Adel Abdul Mahdi) effectively vetoed the 2009 budget law by sending it back to the Council of Representatives which had approved it on March 5.
see Musings on Iraq
UPDATE: The Presidency Council did approve the $58.9 billion budget on 3 April 2009.
see Middle East Times
The Presidency council exists under the transitional provisions in the constitution only during the present term of the first Council of Representatives.
Article 138 states:

First: The expression “the Presidency Council” shall replace the expression “the President of the Republic” wherever the latter is mentioned in this Constitution. The provisions related to the President of the Republic shall be reactivated one successive term after this Constitution comes into force.
Second:
A. The Council of Representatives shall elect the President of the State and two Vice Presidents who shall form a Council called the “Presidency Council,” which shall be elected by one list and with a two-thirds majority.
B. The provisions to remove the President of the Republic present in this Constitution shall apply to the President and members of the Presidency Council.
C. The Council of Representatives may remove a member of the Presidency Council with a three-fourths majority of the number of its members for reasons of incompetence and dishonesty.
D. In the event of a vacant seat in the Presidency Council, the Council of Representatives shall elect a replacement by a two-thirds majority vote of its members.
Third: Members of the Presidency Council shall be subject to the same conditions as a member of the Council of Representatives and must:
A. Be over forty years of age.
B. Enjoy good reputation, integrity and uprightness.
C. Have quit the dissolved (Ba’ath) Party ten years prior to its fall, in case he was a member of it.
D. Have not participated in suppressing the 1991 and Al-Anfal uprisings. He must not have committed a crime against the Iraqi people.
Fourth: The Presidency Council shall issue its decisions unanimously and any member may delegate to one of the two other members to take his place.
Fifth:
A- Legislation and decisions enacted by the Council of Representatives shall be forwarded to the Presidency Council for their unanimous approval and for its issuance within ten days from the date of delivery to the Presidency Council, except the stipulations of Articles 118 and 119 that pertain to the formation of regions.
B- In the event the Presidency Council does not approve, legislation and decisions shall be sent back to the Council of Representatives to reexamine the disputed issues and to vote on them by the majority of its members and then shall be sent for the second time to the Presidency Council for approval.
C- In the event the Presidency Council does not approve the legislation and decisions for the second time within ten days of receipt, the legislation and decisions are sent back to the Council of Representatives, which has the right to adopt it by three-fifths majority of its members, which may not be challenged, and the legislation or decision shall be considered ratified.
Sixth: The Presidency Council shall exercise the powers of the President of the Republic stipulated in this Constitution.

In the next Council of Representatives, to be elected in January 2010, Article 67 to 75 of the Constitution set out that there will be one President, with a largely ceremonial role, without veto power.
Article 73(3) states:

The President of the Republic shall assume the following powers:
. . .
Third: To ratify and issue the laws enacted by the Council of Representatives. Such laws are considered ratified after fifteen days from the date of receipt by the President.