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The United States National Reconnaissance Office have developed a penchant for highly unusual mission patches that commemorate their secretive rocket launches.

I'm convinced that this patch (NROL-28) is based on a movie poster, but what movie is it?

It's hard to know the definitive answer to this.

"NROL" stands for "National Reconnaissance Office Launch", and the missions of these launches are generally classified. The missions' exact purposes and orbital elements are not published, naturally, but often nothing else is divulged either.

It does often seem that the patches carry hidden meanings that refer to the missions' objectives, so the design choices behind the patches are often secret as well. (Of course, this begs the question why the patches aren't just generic ones that can't be analyzed…) Analyzing the data about the launches, including the patches (along with observing the satellites and payloads, of course), is the pastime of many hobby astronomers on the Internet. Says the free, online publication The Space Review in the article Space Age hieroglyphs:

There is considerable anecdotal evidence from the expendable rocket community that patches for classified space missions have long existed, often containing not only inside jokes, but also hints and clues about a rocket’s payload. It would not be too much of a stretch to presume that similar patches may have been created for other classified shuttle payloads as well.

This article, written by two such hobby astronomers, Roger Guillemette and Dwayne A. Day (OK, not that much of a hobbyist), mentions the NROL-28 patch in question (referred to as "figure 8"):

The Trumpet program was apparently followed by a new program featuring somewhat smaller satellites but operating in similar orbits. They continued the reptile motif with the launch of an Atlas V rocket on NRO launch L-28 on March 13, 2008 from Vandenberg Air Force Base. The patch associated with this launch (figure 8) shows Earth in the claws of what appears to be a reptilian hand. The design echoes the posters for the 2005 movie War of the Worlds. (Authors’ correction, 8/28/08: It was brought to our attention that the “reptilian hand” gripping the Earth in figure 8 is, in fact, an eagle’s claw, representative of the bald eagle depicted on the NROL-28 mission patch, now included as Figure 8a).

The War of the Worlds imagery they refer to is this:

And the alternate NROL-28 mission patch they refer to as "figure 8a", which makes the case that the launch patch depicts eagle talons (why that wasn't obvious to the authors already eludes me) is this:

The position of the eagle's four talons on the patch does echo a patch from the "Trumpet program" to which The Space Review referred above (which is reptilian in nature). They write this about that one:

On November 8, 1997, the Air Force launched yet another Titan IV (mission A-17) with characteristics similar to the previous Trumpet mission. This mission patch (Figure 7) featured three cobras wrapped around the Earth. It also featured eleven stars. Notably, the cobras’ bodies and tails seem to indicate both equatorial and high inclination orbits. The Latin phrase—Nunquam Ante Numquam Iteram—cryptically translates to “Never before, never again.”

And this is "figure 7":

As you can see, the cobra's bodies and tails are in roughly the same positions as the talons in the NROL-28 patch, so if The Space Review is correct in their analysis, the NROL-28 patch probably also indicates "both equatorial and high inclination orbits".

This indication which decides the placement of the talons, together with the fact that they wanted an eagle on the patch (and that eagles have three, not four, talons), explains how the NROL-28 patch actually could be a reference to The War of the Worlds even though the imagery is only similar in concept and not so much in appearance.

It's still just conjecture, though.