Usually, people say that thrillers are "taut," which is an odd sort of metaphor. You want your sheets to be taut, if you care about that sort of thing. You want your sails to be taut, if you want the wind to take you anywhere. But why does a book have to be taut? The only thing I can figure out is that tautness implies tension (which is another thing you always hear about thrillers, is that they are tense). A taut rope has a lot of stored-up energy in it, and it may break at any moment, so there's that. So maybe that's what you need in a thriller: energy plus suspense.
The First Assassin is about an attempted (fictional) assassination on Abraham Lincoln that (spoiler alert!) never happened. That takes out a good bit of the suspense right there; you know that the assassin won't succeed. You can still tell the story, though, and do a good job of it, but to do that you are well-advised to keep the story energized. Unfortunately, that doesn't quite happen here.
Johm Miller's The First Assassin manages to do a good job in keeping up the action about half the time. And the action, when it happens, is fairly good. You have a Union officer seeking to keep the President safe, and he is busy in most of the book in ferreting out plots. You have a young, attractive female slave on a Low Country plantation, who is handed a shocking piece of information about an assassin. You have said assassin, a sinister Cuban gun-for-hire, slinking around the mean streets of Washington. All of this is good, and the action scenes, when they happen, are well-written, and well, taut. (That's the word people use. I told you so.)
The problem is that so many parts of The First Assassin are, well, slack. There's an annoying subplot about who will inherit the estate of the South Carolina fire-eater who hires the assassin that could just as easily have been cut out. There is scene after scene after scene where the intrepid Union officer is summoned to meet with General Scott and brief him on what just happened. There's a fairly interesting bit about an American-style Gunpowder Plot that fizzles out and disappears halfway through.
The single most annoying bit of business is the assassin's scheme to kill the President, and how he goes about doing it. Without giving too much away, all you really need is a paragraph to explain what the assassin buys to conceal his weapon, and another two about how he conceals it. What you get is a whole raft of exposition about the people he buys the equipment from, which I guess is there to serve as local color, but mostly just gets in the way of the story.
The characters are something of a mixed bag. Lincoln is here, and if there's any character that's easier to write into a fictional narrative than Lincoln, I'd like to know about him - we know so much of what he says, and his habits, that it's hard to treat him like a regular character in a regular novel. Here, he mostly functions as a quote machine, saying the things we know he said. The Confederate sympathizer who serves as a means for the good guys to track down the bad guys is too phony and self-centered to make much of an impact. The courageous slave girl is there to suffer and not much more.
Where Miller does well in The First Assassin is to tell the historical story of the early days of the Civil War, to make the city of Washington come alive, and to set up action scenes that are lively, gripping, and telling. The First Assassin works on its own merits, but it doesn't transcend them. (That's what you say in a book review when you say that the book is pretty good and you should read it but don't expect too much and you won't be disappointed.)