The mere issuance of a signing statement by a President is not actionable by Congress or anyone else. The President has the freedom to say whatever he wishes about any legislation. And to the extent legislation contemplates the exercise of discretion by the executive agencies in administering the laws (which many do), the President has the right to set administration policy in administering such laws.
Now if the President refuses to enforce legislation that has become a valid law, then Congress has their remedy under the Constitution of impeachment and removal. That was essentially what was attempted against Andrew Johnson, when he failed to follow a law passed by Congress over his veto and which he claimed was unconstitutional (the Sup Ct later agreeing with him).
If Nancy Pelosi wishes to sue President Bush for failing to enforce a law, how about suing him for failing to enforce the laws regarding our border and immigration?