A resolutions committee declined to recommend the controversial resolution to convention attendees, but its key proponent made an unsuccessful attempt to amend another resolution to address his concerns.
Members of the nation's largest Protestant denomination also passed a resolution supporting a federal marriage amendment.
T.C. Pinckney, a former second vice president of the denomination, co-authored a proposed resolution that encouraged Southern Baptists to remove their children from public schools and instead place them in home schools and private Christian schools.
"We owe our children a thoroughly Christian education," Pinckney argued at a microphone on the convention floor. "Government schools are, by law, secular."
Calvin Wittman, the chairman of the resolutions committee, said the 10-member committee prayerfully considered Pinckney's proposal and decided not to bring it to a vote.
"We believe this is a responsibility that God has given to the parents," said Wittman, pastor of a Denver-area church. "We must be careful as a denomination not to usurp the authority that God has placed firmly in the home."
Messengers, or delegates, overwhelmingly rejected the amendment, but the debate on the floor and elsewhere showed strong feelings on the issue.
Larry Reagan, a messenger from Dresden, Tenn., agreed with Pinckney.
"Our children deserve the best," he said. "They need to be taught the truth on Sunday and also on Monday through Saturday."
"If the public school system is our best mission field in America, why would we want to pull all of our Christians out?" asked Welch, pastor of a Daytona Beach, Fla., church.
At that same news conference, Welch announced his plans for a 25-day bus tour in August and September across the United States and Canada to challenge Southern Baptists to be unified in their emphasis on evangelism.
On Wednesday, the messengers adopted several other resolutions, most of which prompted little or no debate.
Without any discussion, messengers passed a resolution urging Southern Baptists to encourage their elected officials to pass an amendment "defining marriage as exclusively the union between one man and one woman."
The statement declared that such a union is "the only form of marriage prescribed in the Bible as God's perfect design for the family" and commended President Bush for his support of a federal marriage amendment.
A resolution on "secularization of our culture" asked Southern Baptists to seek God's forgiveness for their role in "the cultural decline" and said "the cultural drift in our nation toward secularism obscures moral absolutes under the guise of tolerance."
Another resolution on Christian citizenship encouraged Christians to vote "in accordance with biblical values rather than according to party lines, personalities, or candidate rhetoric" and urged churches to hold voter education and registration drives.
Baptists also adopted a resolution of appreciation for former President Ronald Reagan, who died a week and a half before their annual meeting. They said the late president "exemplified the hallmarks of a Christian leader" and they pledged "to perpetuate the positive values so faithfully exemplified" by him.