I'm not going to harp on this anymore. Many people I respect (Chuck Colson, Al Mohler, etc) signed the Manhattan Declaration. However, if you could read only one explanation of why not to sign it, I recommend R.C. Sproul's explanation:
The drafters of the document, Charles Colson, Robert George, and Timothy George, used deliberate language that is on par with the ecumenical language of the Evangelicals and Catholics Together (ECT) movement that began in the 1990s. The Manhattan Declaration states, “Christians are heirs of a 2,000-year tradition of proclaiming God’s Word,” and it identifies “Orthodox, Catholic, and Evangelicals” as “Christians.” The document calls Christians to unite in “the Gospel,” “the Gospel of costly grace,” and “the Gospel of our Lord and Savior Jesus Christ in its fullness.” Moreover, the document says, “it is our duty to proclaim the Gospel of our Lord and Savior Jesus Christ in its fullness, both in season and out of season.”
Without question, biblical truth must be proclaimed and the gospel preached prophetically to our nation. But how could I sign something that confuses the gospel and obscures the very definition of who is and who is not a Christian? I have made this point again and again since the days of ECT. Though the framers of the Manhattan Declaration declaim any connection to ECT, it appears to me that the Manhattan Declaration is inescapably linked to that initiative, which I have strenuously resisted. More than that, this new document practically assumes the victory of ECT in using the term “the gospel” in reference to that which Roman Catholics are said to “proclaim” (Phil. 1:27).
The rest here.