All Dispensationalists are Protestant, but not all Protestants are Dispensationalist. Luther and Calvin were both Amillennialists and I think you’ll find that their eschatology wasn’t really all that different from Catholic or Orthodox eschatology. Later on you find some Postmillennialism showing up in Presbyterianism for a time, although these days you really only see it among the really hard core Christian Reconstructionist types. Historical Premillennialism (that is, Premillennialism that is not Dispensational), started to resurge in the 19th century with the emergence of the Millerites and the Seventh Day Adventists, Jehovah’s Witnesses, and so on.
Dispensationalism, on the other hand, is a relatively new invention. It emerged largely from the teaching of one man: John Nelson Darby, one of the early leaders of the Plymouth Brethren. It remained largely contained within the Plymouth Brethren and few other Independent Fundamental Baptist types until the 1970s when a great many Evangelicals in general and the Jesus People movement in particular latched onto Hal Lindsey’s “The Late Great Planet Earth.” The notion didn’t really enter the popular consciousness, however, until Tim LaHaye (an old school Dispensationalist of the Independent Fundamentalist Baptist type) published the Left Behind series.
One of the features of this later day Dispensationalist Eschatology was a distinct emphasis on the restoration of the State of Israel in 1948 as the start of the “prophetic clock” leading us inexorably towards Doomsday. They say this on the basis of Christ’s Olivet Discourse in Matthew 24, Mark 13, and Luke 21. Specifically, they hang their eschatological hats on the pin of Christ’s warning that “this generation (i.e. the generation that sees the return of Israel, the re-establisment of the Temple, and the Abomination of Desolation) will not pass away until all these things (i.e. the Rapture, the Tribulation, and the Battle of Armageddon) take place.”
Specifically, the chain of logic is thus: They believe that the Abomination of Desolation talked about by Daniel and Christ is the Anti-Christ proclaiming himself to be God in the Temple. That, obviously, can’t happen unless the Temple is rebuilt. The Temple can’t be rebuilt until the nation of Israel is re-established. The nation has been re-estabished and preparations are already under way to rebuild the Temple (seriously, they’ve already made most of the Temple implements and have started training Kohens to serve as an honest to goodness, Old Testament, Aaronic Priesthood), thus the time must be short.
Most evangelicals, or at least most young evangelicals, these days just kind of roll their eyes whenever this stuff comes up. The common phrase you hear is that we are all now “Panmillennialists” in that “Whatever happens, it’ll all pan out in the end.” We’d much rather focus on the more immediate concerns of preaching and teaching the gospel and we’re perfectly happy to let God worry about the details of when He’s coming back to establish His Kingdom, thank you very much.
To put it another way, most young evangelicals these days have no real eschatology. Older evangelicals fall largely into two camps: Those affiliated with the evangelical version of a mainline denomination (i.e. Evangelical Methodists, Lutherans, Presbyterians, and Episcopalians) tend to be Amillennial (or at least their pastors tend to be), while the rest are almost entirely Premillennialists of one sort of another. Within the Premillennialists, most will say that subscribe to something very much like Dispensationalism, right up until you confront them with the problems with Dispensational soteriology and then they’ll deny it. Nevertheless, they’ll still subscribe to a throughly Dispensational eschatology. That having been said, there is a surprisingly large and growing camp of Historical Premillennialist evangelicals that, in the interest of full disclosure, I will say outright that I belong to.