By some estimates, more than 85 percent of Christian congregations in the United States include the word “evangelism” in their mission statements. But some Christian leaders claim surface commitment to what they call the church’s essential task isn’t reflected in the daily lives of those congregations’ adherents -- and it shows.

The much-discussed rise of the “nones” -- the group of one in five Americans who have no religious affiliation—is only the latest evidence cited that evangelism in the United States is in disarray. Church attendance has declined for decades—to about 40 percent, the Gallup organization reports, although some pollsters put the...