One of the conditions to make the brocha on kings is that they have the power to kill you (see Radvaz 1:296 as well as the Orchot Chaim Brachos 49 that say that this brocha is recited on any monarch with enough power to execute or pardon from execution). Although the President could kill someone through different channels (Military, NSA, Secret Service), seemingly that ability could only come clandestily, for if it were ever to come out to light that the President had someone killed he would be subject to impeachment. My question though, is the fact that he can execute someone only come through secret ways enough of a reason to make the Brocha? Is the sheer ability to have someone killed the main criteria according to the Radvaz? Or is it the unquestioned wanton ability to have you murdered the true litmus test to make the brocha
The Radbaz's language (responsum #296) is that he can kill "keMishpat", lawfully. A mob boss, for instance, has the ability to kill, but not lawfully. So I presume if the use of power was totally unlawful for the position, halacha wouldn't consider it. (It doesn't say "he can kill anyone he feels like", or "he can kill you." Just that he can lawfully find people guilty and execute them.)
This is actually a moot point with regards to the US President. Rabbi Ovadia Yosef (Yechave Daat 2:28) and the Piskei Teshuvos on Orach Chaim 224 both feel that the president's power to pardon someone from the death penalty is considered "the power of life and death." (I've read that the framers of the Constitution intentionally gave the US President this power to echo the classical monarchs.)
The Israeli newspapers reported that an ailing Rav Ovadia paskened, on President Obama's last visit to Israel, that the US President's role as commander-in-chief of the army (no secrets there) is also considered "the power of life and death."
(The Tzitz Eliezer, 22:14, disagrees, by the way.)
Lastly, the US President has an additional power of life-and-death: the Justice Department released a memo (again, no secrets here) that if a US citizen joins Al Qaeda and runs off someplace where it's not feasible to capture him, the president can have him killed with a drone strike.
Interestingly, Rav Ovadia and others feel that the President has enough power to warrant the blessing, but not the fancy robes and crown and other trappings. But that's a different question.
In conclusion: Unlawful power would not qualify, but many rabbis feel that the US President has sufficient non-secret power to warrant the blessing.