This video blogger asserts that "John Calvin was Martin Luther's greatest student." Calvin held Luther in high regard and there certainly are a number of theological agreements between these two men. But I would not go so far as to suggest, as this video blogger does, that Calvin followed Luther's view on the extent of the atonement as his greatest student. There's stronger evidence that suggests that it was, to a large extent, fellow Reformer Martin Bucer and an Augustian tradition that influenced Calvin on the extent of the atonement, not Luther.
The debate over the historicity of the doctrine of limited atonement is complex. It's actually more complex in regard to Calvin's view rather than Luther's. There are a number of scholars who argue Calvin did not hold to the doctrine of limited atonement. Then there are a number who argue the contrary. There are also typically two sorts of people who get involved with this controversy. Those in the first group are interested in history and in following the strands of evidence wherever it leads. They can either be Reformed or non-Reformed, and they can arrive at either position regarding Calvin's view. In the second group are those who are looking to refute Reformed soteriology by arguing Calvin himself did not hold to limited atonement (i.e. Geisler, etc.).
Jonathan Rainbow points out, "There is no single place where Calvin addressed the extent of Christ's redemption in a systematic fashion" (The Will of God and the Cross, p. 64). This means that each group of scholars arrives at their conclusion based on exegeting the strands of evidence throughout Calvin's writings. Rainbow points out that Calvin was never involved in any controversies involving the extent of the atonement. As far as I know, neither was Luther. This certainly means it requires much more work to sort out their views. Certainly by the late Sixteenth Century Lutheranism opposed limited atonement, while the Reformed tradition by the early Seventeenth Century embraced it with confessional statements (Rainbow, pp. 181-182). For what it's worth, I think Rainbow has presented one of the best constructed non-polemical treatments of Calvin's view.
If Calvin's view requires a lot of work to figure out, the evidence in regard to Luther's view is even more difficult to sift through. The simple truth is that, contrary to my Reformed brethren, Luther's writings are not filled with comments about predestination, election, and the extent of the atonement. Certainly Luther's Bondage of the Will gets involved with predestination, but if you set out to read Luther writings you'll find that these soteriological issues so important to Reformed theology don't get center stage in Luther's treatises.
This video-blogger cites Luther’s early work on Romans. There Luther comments on “God will have all men saved” (1 Tim 2:4). He says that sayings like this “must be understood only with respect to the elect” and that “Christ did not die for absolutely all.” From such comments it appears easy to conclude Luther taught limited atonement. But here's the crucial factor, as I see it: Other than this pre-reformation comment, there is no other evidence I know of that Luther maintained such a view throughout his life on the extent of the atonement.
Luther would instead go on to say things like, “[Christ] helps not against one sin only, but against all my sin; and not against my sin only, but against the whole world's sin. He comes to take away not sickness only, but death; and not my death only, but the whole world's death.” For Luther, the revealed God did indeed die for the sins of every human being. Quotes similar to this are peppered throughout his later writings. For Luther, the Scriptures state that Christ died for all men and not all are saved. Nevertheless, Christ died for all men, and wants all men saved.
I maintain that it appears, based explicitly on this one quote, and implicitly from Luther's early work on Romans, that limited atonement was an early view Luther held. His later writings strongly imply a different conclusion on the extent of the atonement. Those people (particularly Reformed people) use the Romans commentary quote at the expense of Luther's entire written corpus, thus caricaturing his view. It is typically the only quote they use, and I challenge them to search through Luther's writings to find another. I certainly would be interested in any quotes they find... I'm doubtful though anything like Luther's Romans quote exists.