I will not use signing statements to nullify or undermine congressional instructions as enacted into law. The problem with this administration is that it has attached signing statements to legislation in an effort to change the meaning of the legislation, to avoid enforcing certain provisions of the legislation that the President does not like, and to raise implausible or dubious constitutional objections to the legislation. The fact that President Bush has issued signing statements to challenge over 1100 laws – more than any president in history – is a clear abuse of this prerogative. No one doubts that it is appropriate to use signing statements to protect a president's constitutional prerogatives; unfortunately, the Bush Administration has gone much further than that.
There are two important points in his answer, and unfortunately the focus has only been on one part. Obama says that he will not use the signing statement to "nullify or undermine congressional instructions enacted into law." Now if you use just this standard, any constitutional challenge in a signing statement by definition will either nullify or undermine congressional intent. You have to partner it with a key second part: "No one doubts that it is appropriate to use signing statements to protect a president's constitutional prerogatives."
The constitutional signing statement is designed to challenge provisions that either intrude upon the prerogatives of the president or violate the rights of states or individuals. Under the principle of coordinancy, it is the obligation of each branch of government to determine the meaning of the Constitution and the powers it is given. The Congress and the presidency have been pushing the boundaries of their respective powers since 1789 and will continue to do so in the future. To insure that a push does not "stick," the president has made use of the signing statement to declare that certain provisions violate his prerogatives--the formation of hybrid commissions, the power to recommend, the power to appoint, the power to establish foreign policy, etc. The Bush II administration decided to use the constitutional signing statement, without congressional objection, to make broad claims about the power of the presidency--claims that were not seen as legitimate by most people.
Obama clearly claimed both in December 2007 and in his March 2009 memo on the use of the signing statement that he would revert to the more traditional use of the signing statement--to protect his prerogatives and the rights of states/individuals, and not to upset the clear intention of the Congress for political purposes or to make illegitimate claims of presidential power. You may ask what the first part means--making claims for political purposes?
Presidents have run into trouble when they attempt to use the signing statement to negate a battle lost in the Congress. For instance, the Reagan administration made a change to a controversial provision of the 1986 Immigration Reform and Control Act that revised a provision dealing with discriminatory firing. The provision was designed to allow fired employees to sue based on discrimination, placing the burden of proof on the employer. Because the provision was not clearly defined, the Reagan administration used the signing statement to define the provision so it placed the burden of proof on the fired employee. Then in 2002, the Bush administration defined the whistleblower provision of Sarbanes Oxley so narrowly that it provoked outrage in the Senate--Senators Leahy and Grassley pressured the administration to back away from the provision, which the administration did temporarily.