According to Baptist Calvinist, J.B. Jeter, Andrew Broaddus (1770-1848) remained a Baptist legend in 19th century Virginia. Broaddus’ rhetorical skills and keen intellect apparently made him a theological "genius" of sorts (p.45). Jeter's description of Broaddus surely places him in the position of being one of the most influential Baptists during the first half of the 19th century.
In his Sermons and Other Writings, Broaddus indicated concerning infant baptism and infant salvation:
“If there were no other way of saving infants but by the gospel and its ordinances, they would be excluded from salvation; for with them the gospel and its ordinances have nothing to do. Infants are saved by virtue of the death of Christ, but not by faith—not by the gospel. And you do not gather them into the promise by baptism, for the promise is to him that believeth and is baptized. God has committed the ministration of the gospel and its ordinances to us; but the salvation of infants he has reserved in his own hands” (pp.189-190. italics original)
-- Andrew Broaddus, Sermons and Other Writings of the Rev. Andrew Broaddus, With a Memoir of his Life by J.B. Jeter, D.D. Edited by A. Broaddus, Son of the Author and Minister of the Gospel. New York: 1852.