Doug Liman’s new sci-fi blockbuster is burdened with a terrible title that makes it sound like a cousin to the old ABC soap opera “Edge of Night,” action sequences that recall the blurry excesses of “Jumper” rather than the excitement of the early Bourne pictures, and a postscript that only proves that today’s filmmakers will go to any lengths (however incomprehensible) for a happy ending. Still, “Edge of Tomorrow” is slightly more clever than most of its big-budget brethren, and in its early stages it has an engaging sense of humor that unfortunately grows increasingly infrequent later on.

The movie begins promisingly, with a montage quickly depicting the takeover of Europe by a race of vicious aliens called Mimics that arrived in what first appeared to be a wayward asteroid. Imbedded in the footage are shots of Maj. William Cage (Cruise), a super-smooth army spokesman who’s great at putting the best face on defense efforts and encouraging folk to volunteer for combat duty. He finally has some good news to report when a single soldier, Rita Vrataski (Emily Blunt) has single-handedly managed to kill hundreds of the speedily-slithering, multi-tentacled creatures at Verdun (which, of course, just happens to have been the site of the bloodiest battle on World War I’s Western Front). Building on her triumph, Gen. Brigham (Brendan Gleeson), the no-nonsense head of the international force being mounted in England against the extraterrestrials, plans a D-Day style invasion on the beaches of Normandy.

But he adds a wrinkle to the operation, telling Cage, a slick salesman who’s never been in the field, that he’ll be joining the first wave. Cruise has played the callow fellow with such oily charm that one can understand why the general would want to put him into harm’s way, but it still seems more like a plot device than a serious military decision. Nevertheless one appreciates it, however unlikely, because it puts the now-panicked Cage in the charge of Sgt. Farrell Bartolome, a tough-as-nails disciplinarian played by Bill Paxton with a delightful sense of mischief. Told that Cage is a deserter impersonating an officer, the sergeant plunks him in with the misfits of the company assigned to lead the assault in their Transformers-like metallic battle suits. Unfortunately, it turns out that the Mimics are ready for the invasion, which turns into a slaughter. Cage is killed, though not before overcoming the odds to kill a particularly big, nasty alien and being soaked in its corrosive blood.

Two things must be noted here. One is that the invasion sequence, with its World War II connotations, is both a little tasteless and the first instance in the picture of a deliberately muddled-up action set-piece, with events swirling around so messily (and made murkier by the 3D effect of darkening the images) that it’s often difficult to tell what’s actually happening. (Things do slow down enough to let us see the Mimic clearly for the first time, looking like a much more filled-out version of the then-cutting-edge monster from “Forbidden Planet.”) It’s a visual crutch that “Edge of Tomorrow,” like so many of today’s CGI extravaganzas, will employ repeatedly. Some will say that it’s to make the scenes more viscerally exciting, but one can’t help harboring the suspicion that the real reason is to obscure the fact that the effects are not all that convincing.

Anyway, it’s at this point that the plot kicks in, as Cage reawakens, “Groundhog Day” style, to find himself at the beginning of the unhappy day again. If one is permitted a certain flippancy, he might say that the narrative takes one from alpha to omega: the special Mimic that Cage killed was what scientist Dr. Carter (Noah Taylor) calls an Alpha, the sort that in effect controls its smaller comrades on the battlefield. But it is in turn controlled by the Omega Mimic, a bulging brain behind all the alien operations that has the capability to rewind time whenever an Alpha is killed. And now that Cage’s blood has been mingled with the Alpha’s, it means that whenever he dies, the Omega will rewind time to the beginning of invasion day again.

It turns out that the same thing had happened to Vrataski, as Cage will learn when after several rewinds he seeks her out. It was what allowed her success at Verdun; but since then she’s lost the ability. While she possessed it, however, she glimpsed where the Omega is situated, and she and Carter have determined that only killing it will end the Mimic menace to earth. So she undertakes to train Cage in combat and accompany him on literally repeated invasions of the coast so that they can learn through repetition to avoid being killed and eventually make their way to the Omega’s lair to destroy it.

Here Liman dexterously changes his chronological approach. In the early going he portrays various unsuccessful invasion scenarios in considerable detail, to get viewers completely situated in the premise. Now he moves forward much more rapidly, only giving a taste of moments from further attempts by the pair, often leavened with humorous twists, to suggest how many hundreds, if not thousands, of times they’ve gone through the same day. There are stumbles along the way—because apparently the Omega can hide its location with false visions—that necessitate a trip to a suspicious Gen. Brigham that threatens to derail the mission completely. But eventually Cage and Vrataski persuade the men of his old company of misfits to join with them on a desperate mission to take on the Omega and its many defenders at the Louvre in Paris, where the creature has secreted itself beneath the famous Pyramid. (You will be happy to learn that the Omega is not being defended there by an albino named Silas.)

Despite the best efforts of Liman, scripters Christopher McQuarrie and Jez and John-Henry Butterworth, cinematographer Dion Beebe and editors James Herbert and Laura Jennings, this longish segment of the movie, while managing to minimize the repetitiveness of the action by emphasizing surprising, often amusing, jolts rather than the banality of seeing the same bits over and over again, doesn’t capture Cage’s learning process especially well. The transformation of the inept fellow into the heroic Cruise-control model on which the last act of the picture will coast is curiously abrupt and unconvincing. And, of course, time must be taken for the obligatory romance that gradually blooms between Cage and Vrataski. Nor is the action at the Louvre especially well handled; set at night, the entire sequence is even murkier than the invasion ones, though the loping, spidery Minions do look great. The postscript that follows, on the other hand, is obviously designed to send the audience home with assurances that not only has the world been saved but true love has triumphed—but one must ask: how, and at what cost? The solution the filmmakers have come up with comes across as farfetched as, and no less disappointing than, the one Richard Donner used in the original “Superman” (and intended to use in his version of “Superman II” as well).

Most viewers may be willing to put up with that, however, in return for a big action movie that’s slightly smarter than most, though not smart enough to convince you that the premise wasn’t better suited to a Bill Murray comedy than a Tom Cruise sci-fi behemoth. They may also appreciate Cruise’s willingness to send up his toothy slickness, especially in the first act; and men of a certain age will certainly admire a man of his years still capable of handling the physical demands of the role. Apart from Paxton—who, between this and “Million Dollar Arm” shows the extent of his range—and to a lesser extent Gleeson, the rest of the cast don’t have much opportunity to shine, including Blunt, who’s given little more than standard-issue she-ro tasks to perform. The production team—including designer Oliver Scholl, the large art direction team led by Neil Lamont, set decorator Elli Griff along with Beebe, Herbert and Jennings—all contribute capable work, if one sets aside those jittery, over-cut action sequences; and Christophe Beck’s score is better than his usual work, though in the IMAX sound system it’s often overbearing.

In sum, “Tomorrow” is moderately engaging, but not up to the level of really outstanding summer action fare. You could say that it’s on the very edge of being a winner.