The truth, as is so often the case, is found in neither narrative. The confusion stems at least in part from the fact that the resolution on the "sinner's prayer" that was widely touted by neo-traditionalists before the convention was completely different from the one that came out of committee and was ultimately adopted by the messengers. The one that Eric Hankins submitted was problematic for many reasons. The one that was presented and adopted was much more carefully worded and grounded in biblical language and reasoning.
There were some who spoke against the resolution that made it to the floor, primarily due to the damage that superficial evangelism (which often uses a form of words "as an incantation that results in salvation merely by its recitation") has done to individuals and churches. This, however, is far from a "Calvinist" concern. Nor would it be accurate to evaluate the passing of this resolution as a slap against the more reformed elements in the convention.
The most impassioned statement made during the debate was by Mitch Axsom, an elder at First Baptist Church of Clinton, Louisiana. That 175 year old church's confession of faith is the 1689 Baptist Confession and Mitch spoke for the resolution.
To make it easier for you to compare the resolution that was submitted to the one that was adopted, I have reproduced them both below. Hopefully, this will help clear up some confusion and prevent further misrepresentation of what happened in New Orleans regarding the "sinner's prayer" resolution.
This is the resolution that Eric Hankins submitted:
WHEREAS, God desires for every person to be saved and has made salvation available for any person who hears the Gospel (John 3:16; Romans 10:14-17; 1 Timothy 2:3-4; 2 Peter 3:9; 1 John 2:2); and
WHEREAS, A free response to the Holy Spirit’s drawing through the Gospel is both possible and necessary in order for anyone to be born again (John 3:1-16; Acts 16:30-31; Romans 10:11-13; 1 Thessalonians 2:13); and
WHEREAS, Prayer is God’s gracious means through which any person can communicate with Him and is everywhere in Scripture commanded and commended for every matter and every person (2 Chronicles 7:14; Matthew 7:7-11; Mark 11:17; Philippians 4:6); and
WHEREAS, Praying to God to express repentance for sins, to acknowledge Christ as Lord, and to ask for forgiveness and salvation is modeled in the Bible (Acts 2:37-38; Romans 10:9-10); and
WHEREAS, While there is no one uniform wording found in Scripture or in the churches for a “Sinner’s Prayer,” the prayer of repentance and faith, acknowledging salvation through Christ alone and expressing complete surrender to His Lordship, is the biblical means by which any person can turn from sin and self, place his faith in Christ, and find forgiveness and eternal life (Luke 18:9-14, 23:39-43); and
WHEREAS, It is biblically appropriate to help a sinner in calling on the Lord for salvation and to speak of Christ’s response to such a prayer as “entering a sinner’s heart and life” (John 14:23; Acts 2:37-40; 16:29-30; Romans 10:11-17; Ephesians 3:17); and
WHEREAS, A “Sinner’s Prayer” is not an incantation that results in salvation merely by its recitation and should never be manipulatively employed or utilized apart from a clear articulation of the Gospel (Matthew 6:7, 15:7-9; 28:18-20); now, therefore, be it
RESOLVED, That the Southern Baptist Convention, meeting in New Orleans, LA, June 19-20, 2012, commend the use of a “Sinner’s Prayer” as a biblically sound and spiritually significant component of the evangelistic task of the church; and be it further
RESOLVED, That we encourage all Christians to enthusiastically and intentionally proclaim the Gospel to sinners everywhere, being prepared to give them the reason for the hope we have in Christ (I Peter 3:15), and being prepared to lead them to confess faith in Christ (Romans 10:9), including praying to receive Him as Savior and Lord (John 1:12).
This is the resolution that the SBC adopted:
AN AFFIRMATION OF A “SINNER’S PRAYER” AS A BIBLICAL EXPRESSION OF REPENTANCE AND FAITH
WHEREAS, The Gospel of Jesus Christ offers full forgiveness of sins and reconciliation with God to anyone who repents of sin and trusts in Christ; and
WHEREAS, This same Gospel commands all persons everywhere to believe this Gospel and receive Christ as Savior and Lord (Mark 1:15; John 1:12; 6:25–52; Acts 17:30); and
WHEREAS, The Scriptures give examples of persons from diverse backgrounds who cried out for mercy and were heard by God (Luke 18:13; Acts 16:29–30); and
WHEREAS, The Scriptures also give numerous examples of persons who verbally affirmed Gospel truths but who did not personally know Jesus in a saving relationship (Luke 22:47–48; John 2:23–25; 1 Corinthians 10:1–5); and
WHEREAS, Empty religion and formalism, of whatever kind, apart from personal relationship with Christ, cannot wash away sin or transform a heart (Matthew 7:21; 15:8; John 3:3); and
WHEREAS, The Bible speaks of salvation as including both a confession with the mouth that Jesus is Lord and a belief in the heart that God has raised Him from the dead (Matthew 16:16; Romans 10:9–10); now, therefore, be it
RESOLVED, That the messengers to the Southern Baptist Convention meeting in New Orleans, Louisiana, June 19–20, 2012, reaffirm our Gospel conviction that repentance from sin and personal faith in the Lord Jesus Christ are necessary for salvation (Acts 20:20–21); and be it further
RESOLVED, That we affirm that repentance and faith involve a crying out for mercy and a calling on the Lord (Romans 10:13), often identified as a “sinner's prayer,” as a biblical expression of repentance and faith; and be it further
RESOLVED, That a “sinner’s prayer” is not an incantation that results in salvation merely by its recitation and should never be manipulatively employed or utilized apart from a clear articulation of the Gospel (Matthew 6:7; 15:7–9); and be it further
RESOLVED, That we promote any and all biblical means of urging sinners to call on the name of the Lord in a prayer of repentance and faith; and be it finally
RESOLVED, That we call on Southern Baptists everywhere to continue to carry out the Great Commission in North America and around the world, so that sinners everywhere, of every tribe, tongue, and language, may cry out, “God be merciful to me a sinner” (Luke 18:13).