Scott McLemee has described Richard Sennett in the following terms, which I think are accurate and to the point: "Sennett’s work, if not Marxist, is at the very least grounded in some notion of mankind as the species that creates itself through the labor process."

I think this specification of what Sennett (minimally) owes to Marx is valuable because, although it is relatively simple, this notion of self-creation-through-labor is often what seems to go missing when people go hunting for Marxism or Marxian ideas around the Left, looking for ammunition either to smear leftists or to reinvigorate them.

The idea that humankind creates itself through the labor process is not, I suppose, a terribly radical notion, and for that reason, perhaps, it is not very central to many of the most illustrious Marxist or Marxian projects of our day. It disappears behind "fidelity to the event" within Badiou, and gets constantly screened out by Žižek's Lacanianism. I haven't read enough of Negri/Hardt to say for sure, but their conception of the multitude, from what I understand of it, seems to focus on autonomy in a way that very well may be antithetical to this notion.

I think Sennett addresses this fact obliquely within his own personal history: he begins these lectures (the material of the book was originally presented as The Castle Lectures at Yale) by reflecting on his eager participation in the New Left, and notes that the principles espoused most concretely in the Port Huron Statement have, in a sense, been fulfilled, but with results quite opposite to those wished.

The goal for rulers today, as for radicals fifty years ago, is to take apart rigid bureaucracy.
The insurgents of my youth believed that by dismantling institutions they could produce communities: face-to-face relations of trust and solidarity, relations constantly negotiated and renewed, a communal realm in which people became sensitive to one another's needs. This certainly hasn't happened. The fragmenting of big instititutions has left many people's lives in a fragmented state: the places they work more resembling train stations than villages, as family life is disoriented by the demands of work. Migration is the icon of the global age, moving on rather than settling in. Taking institutions apart has not produced more community. (2)

Sennett doesn't press too hard on this point—the New Left's values foreshadowing those of the New Capitalism—though he uses very similar terms to those above in conclusion, returning to this historical irony. (Some of the work of making this irony more concrete is provided by Thomas Frank in The Baffler and The Conquest of Cool, although I wonder if Sennett might see the congruence of the New Left and New Capitalism on this question to be less collusive than Frank tends to paint it.)

At any rate, I think it is important to keep in mind that Sennett is using the New Left as a point for pushing off; these lectures are, in part, arguing that what the New Left failed to account for in their critique of bureaucracy is precisely what must be salvaged—the value of narrative (as in personal narrative), usefulness, and craftsmanship. It is these three values which he believes are most threatened by the new capitalism, as they are being purposely driven out of the workplace under three challenges:

The first concerns time: how to manage short-term relationships, and oneself, while migrating from task to task, job to job, place to place. If institutions no longer provide a long-term frame, the individual may have to improvise his or her life-narrative, or even do without any sustained sense of self.
The second challenge concerns talent: how to develop new skills, how to mine potential abilities, as reality's demands shift… The emerging social order militates against the ideal of craftsmanship, that is, learning to do just one thing really well; such commitment can often prove economically destructive. In place of craftsmanship, modern culture advances an idea of meritocracy which celebrates potential ability rather than past achievement.
The third challenge follows from this. It concerns surrender; that is, how to let go of the past. The head of a dynamic company recently asserted that no one owns their place in her organization, that past service in particular earns no employee a guaranteed place. How could one respond to that assertion positively? A peculiar trait of personality is needed to do so, one which discounts the experiences a human being has already had. This trait of personality resembles more the consumer ever avid for new things, discarding old if perfectly serviceable goods, rather than the owner who jealously guards what he or she already possesses. [I'd say it more resembles a fantasy baseball manager—or an armchair stockbroker.]
What I want to show is how society goes about searching for this ideal man or woman… A self oriented to the short term, focused on potential ability, willing to abandon past experience is—to put a kindly face on the matter—an unusual sort of human being. Most people are not like this; they need a sustaining life narrative, they take pride in being good at something specific, and they value the experiences they've lived through. The cultural ideal required in new institutions thus damages many of the people who inhabit them. (4, 5)

That (long) passage acts as a very good prospectus for the rest of the book; Sennett bears down on this question in an extremely orderly manner, and takes his time filling in the picture of this culture. At times, much of what he says is extremely familiar—both in the way of description and in the way of critique. Yet it is not over-familiar, and it is so well-stated and so well-organized that the value becomes not so much the insight as the articulation—the book is indispensable because it accumulates all the stray thoughts and angles and observations, seeing clearly the larger shape which each one partially illuminates.

Which is not to say that Sennett's insights aren't powerful and frequently new; I think that his chapter on politics as consumption adds some particularly original ideas to that general idea, and some of them have become much more interesting (and ambiguous) after the last election.

I like this book a lot; I think it is tremendously instructive, and is as purely illuminative of some extraordinarily complex formations as you're ever likely to find.

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Speaking of The Baffler, Twitter tells me that it's being revived!