In Didache 7:1-4, we read the following:
And concerning baptism, thus baptize ye: Having first said all these things, baptize into the name of the Father, and of the Son, and of the Holy Spirit, in living water.
2 But if thou have not living water, baptize into other water; and if thou canst not in cold, in warm.
3 But if thou have not either, pour out water thrice upon the head into the name of Father and Son and Holy Spirit.
4 But before the baptism let the baptizer fast, and the baptized, and whatever others can; but thou shalt order the baptized to fast one or two days before.
It is verses 3-4 that we will focus upon in this post.
According to some defenders of baptism by sprinkling being a valid mode of baptism, the Didache is an early witness for such. However, it should first be noted that the Didache is showing that the manner of baptism is an exception to the rule and not the norm, and should only be the case if/when enough "living water" is available (something most modern Churches, regardless of denomination, do not fall under). In the Bible itself, exceptions to the norm are often allowed. Note, for instance, in 1 Sam 21:6 and David’s consumption of shewbread, which was typically consecrated for only the high priests.
Secondly, one could argue that a form of immersion is still in view. One can imagine that someone is in a body of water, but not enough for "normal" immersion, so one having water poured out on them during baptism to ensure some type of full-body immersion during the baptism. While not the only plausible interpretation, it is not impossible (though I am not wedded to it). Some scholars, though a minority, have held a similar view, most notably Eduard Stommell.
Thirdly, it has been noted by scholars that the author(s) of the Didache was strongly influenced by Jewish practices. As one scholar noted:
Most attention is paid to the kinds of water used, which should be pure, running ("living") water if possible (compare the six grades of water in m. Miqw. 1:1-8). The implication is that baptism is a ritual purification from uncleanness. (Jonathan Draper, “Didache” in The New Interpreter’s Dictionary of the Bible, volume 2: D-H [Nashville: Abingdon Press, 2007], 123)
Such would require the entire body coming into contact with water, not a part thereof, in light of such a Jewish background.
Everett Ferguson, commenting on baptism in the Diadache, wrote:
The whole account in the Didache presupposes the baptism of persons of responsible age: those who received detailed instruction in the moral life, those who fasted, and those who joined in the communal eucharist (9-10) . . . Baptize has its normal meaning of “immerse.” This was to be done “in living (running or moving) water.” The valuation of different kinds of water is another indication of the Jewish environment of the Didache. Running water was called “living” because it had motion. Such water was the appropriate place for an act that imparted life (spiritual). “Living” or “life” is an important concept for the compiler of the work. Christians serve a living God (6.3) by walking in the way of lie (3-4) and giving thanks for lie and immortality (eternal life) made known through Jesus (9.3; 10.3).
If running water was not available, other water, that is, collected water, could be used. Apparently some question was raised in the community about the suitability of other kinds of water, and provision was made for accepting alternatives. Cold water was that gathered in a natural pond or lake; warm water was stored in a man-made place (as a cistern or a mikveh). In the absence of a sufficient amount of water (whether from a flowing source or still) for covering the body, water would be poured over the head, as representing the whole of the body, or since the person was likely standing, in order for it to run down the rest of the body. The apparently real possibility of a scarcity of water suggests a provenance such as rural western Syria. (Everett Ferguson, Baptism in the Early Church: History, Theology, and Liturgy in the first five centuries [Grand Rapids, Mich.: Eerdmans, 2009], 203-5.
Interestingly, Ferguson does note that there is a possibility that we could be dealing with an interpolation to the Didache:
The change from the second person plural (7.1) to the second person singular (7.2-3) may mark an addition from another source or an addition by the compiler of the present form of the text; other such changes occur at seams that commentators see in the text of the Didache. The fourth-century compiler of the Apostolic Constitutions used the Didache as the basis for his seventh book. The section on baptism (7.22) does not include the instructions on different kinds of water or on thhe possibility of pouring; he may have found them no longer relevant in a time of of baptisteries, have objected to them, or perhaps not have found this section in his copy of the Didache. If the section with these alternatives was an interpolation, its date cannot be established. The only complete text is the Jerusalem manuscript 54 (Byrennios), dated 1-56, and the Georgian version, possibly derived from the fifth century. The continued Jewish concern with the relative value of types of water indicates that the section, whether part of the redactional activity of the compiler of the Didache or a later insertion into his text, was still quite early, likely no later than the second century (Ibid., 206)
Regardless of the plural possibilities, Catholic and other (e.g., Presbyterian) defenders of sprinkling as a valid form of baptism have to latch on to a possible exception in a non-inspired text, one that most of the Western world does not face and go against what the Didache itself presents as normative (in such circles, baptism by immersion is the rare exception to the rule). Furthermore, one will have to fly in the face of the explicit biblical teachings on the proper mode of baptism, such as Rom 6:1-5. Such apologists are in a truly unenviable position.
