I'm thankful that Paul Trebilco has done the research for me in his book Self-designations and Group Identity in the New Testament (Cambridge, 2012). Trebilco here includes chapters on ἀδελφοί, the believers, οἱ ἅγιοι, ἡ ἐκκλησία, μαθηταί, ἡ ὁδός, and Χριστιανός. So far I have read only the chapter on the μαθηταί, which is excellent. Here I'll give a few notes and excerpts.
Trebilco concludes that Jesus did use the term 'disciples' (the Aramaic talmidayya) for his own followers, but he defined this in a very narrow way: to be a disciple of Jesus meant to literally follow him around, leaving homes and facing persecution. But one did not necessarily have to be a 'disciple' of Jesus (in this narrow sense) to be an adherent of Jesus' teaching. Some people in the Gospels are represented as staying in their homes and still supporting Jesus, though the word 'disciple' would not apply to them.
These [‘sedentary supporters’] are people who did not leave their homes but rather offered Jesus hospitality when he visited their town--people like Zacchaeus (Luke 19:1-10), Lazarus (John 12:1-2), Mary and Martha (Luke 10:38-42; John 11:1-45; 12:1-8), and the anonymous host of the Last Supper (Mark 14:13-15). Decisively, these people are not called ‘disciples’ in our Gospels; they ‘lack the conditions … necessary for being considered disciples’ [citing Meier, p. 80]--a call from Jesus, abandonment of home and family, the risk of danger and hostility. Everyone who was in some way a ‘committed adherent’ is not thereby necessarily called a disciple. (p. 219)Trebilco believes that it is because Jesus used the term 'disciple' in such a narrow sense that it did not become popular in earliest Christianity to designate believers generally. Paul, for instance, apparently felt it inappropriate to use the term 'disciples' for Christians in Ephesus, or Galatia, or Rome, since they were not literally following Jesus and had not actually left their households and livelihoods. Trebilco goes on to suggest that the term ‘disciple’ was too weak for Paul to express what he meant by being committed to Jesus. Rather, Christ lives in me. Moreover, ‘disciples’ might live separately, but Paul needed to emphasize community, and so family language and ἐκκλησία worked better. Finally, as Jesus was no longer thought of as a διδάσκολος (never used of him outside the Gospels), so his adherents were not thought of as disciples.
The usage in Acts is owing to Luke's theological program to show continuity between the earliest church and the time period of Jesus. Trebilco also sees various indications in the Gospels--at least, Matthew, Luke, and John--that the Evangelists wished for Christians in their own day (a generation or more after the time of Jesus) to think of themselves and call themselves 'disciples'. This is most clear with the broadening of the term 'disciple' in Luke 6:17; 19:37, the use of the verbal form in Matt 28:19 (cf. 13:52; 27:57), and the very different way of defining 'discipleship' in John.
So, although μαθηταί in John 1:35-51 are called by Jesus to ‘follow me’, and they do this literally (e.g., John 1:37; 2:12; 3:22), in some passages in the Gospel being ‘disciples’ is defined more broadly so that it involves other things that are not tied to itinerancy (such as ‘continuing in my word’, loving one another and being loved by Jesus) or in fact to being present with the historical Jesus and so can apply to a larger group. (p. 241)Mark is the only Gospel for which it is not clear that he wants his readers/hearers to think of themselves as ‘disciples’, though Mark 13:37 implies that Mark wanted his audience to put themselves in the place of Jesus' disciples and recognize that (some of) the teachings delivered to the original disciples also applied to the later church.
Trebilco then goes one step further, into the Apostolic Fathers to see if anyone at that time had started using the term 'disciples' for Christians generally. The terms μαθητής and μαθητεύω are absent from the Apostolic Fathers except for Ignatius (noun 9x, verb 4x) and The Martyrdom of Polycarp (noun 2x). Ignatius is especially interesting because several times he links discipleship to martyrdom (his own), thus reflecting the ‘cross-bearing’ sayings in the Gospels and perhaps Luke 14:27. But Ignatius can also use the noun for all Christians. The same is true, later, for Justin (p. 245 n. 213). So Ignatius re-introduces the term as a general one for Christians perhaps having picked up on this theme in the Gospels. But he is the only one at this early time.