What the f... does the title have to do with the plot? (spoilers)

Caesar thought he was untouchable. He thought he was in control. All those congressmen plotted behind his back took a lot of political maneuvering. This movie is about all the backstabbing that goes on in the political world. It's metaphorical, not literal.

Stephen's ideals are ultimately assassinated.

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Joe Satriani - "Always With Me, Always With You"
https://y2u.be/VI57QHL6ge0

Let's try this. The movie is loosely based on Shakespeare's Julius Caesar; that seems to be a given. I think the main characters are based on characters from that play, though maybe not in the way you'd think. Brutus is the noble and idealistic statesman who falls from his nobility and is corrupted. That's Mike Morris. Cassius is the schemer who brings down Caesar and corrupts Brutus. That's Stephen Meyers. And Caesar, the one who is overthrown by men he trusts? That's Paul Zara--surprise, surprise! Senator Thompson, Tom Duffy, and others are other miscellaneous conspirators. It's a loose adaptation of Julius Caesar, so none of the parallels is perfect, nor do they have to be. In the play the warning about the Ides of March is meant to Caesar about impending disaster. I think the nearest parallel is the scene when Zara fires Meyers. He doesn't realize the warning signs inherent in antagonizing such an intelligent and driven man. The stabbing occurs in the backseat of Morris's car, off camera. Brutus, or Morris, figuratively assassinates Caesar, or Zara.

I can find no Marc Antony, since no character steps forward to defend Zara with the intent of replacing him. Maybe the producers and writers saw Meyers as a blend of Cassius and Antony. Where does Molly fit? She isn't Calpurnia, Caesar's wife, or Portia, Brutus' wife. I think that this promiscuous young woman and the excessive foul language are in the movie to attract the modern audience that enjoys such things.

There are some old threads (probably deleted by now) in which people fall all over themselves in trying to interpret the movie via the title.

Anyway, my answer to the question is consistent with the implication in the first few words of the way you framed it:

The title doesn't have much, if anything, to do with the plot.

The reasons I can think of for the title:
- Just the nifty coincidence that it takes place in the middle of March (which is approximately consistent with the timing of the real Ohio primary).
- The title conveys the message that it's serious and dramatic, rather than a fun movie or even a humorous satire.
- Some vague thematic connections: disloyalty, politics, abuse of power and position.
- Sense that it's a tragedy. I guess that's sort of a story connection, but not much of one. In the play bunches of people die (as they tend to do in Shakespeare tragedies); in the movie one person - who bears no connection to anyone in the play - dies, but the tragedy has more to do with the loss of ideals ... that sort of thing.
- Sounds important, and the movie is supposed to be important (whether or not it actually succeeds in being thus).

There's an obvious answer to those who think that the movie was written with a story based on "Julius Caesar:" the movie is an adaptation of a play which wasn't named "The Ides of March," but "Farragut North." The story preceded the title.