The thesis and tone of The Swerve echo Jacob Burckhardt's now somewhat discredited 19th century characterization of the Italian Renaissance with its celebrations of life and beauty as a "return to paganism" (as though the Middle Ages didn't have its festivals and gai savoir). Burckhardt's book may be outdated as history but is nevertheless a masterpiece of Romantic historiography that repays rereading. Greenblatt is no Burckhardt, but it sounds like his book will also be valuable - even only insofar as it is successful in familiarizing contemporary readers with the role of characters like the colorful Poggio Bracciolini, Lorenzo Valla and their manuscript-hunting Humanist confreres, many of whom were employees, like Poggio himself, of the Papal court.
Greenblatt seriously overstates the role of Lucretius, whose influence, until the mid to late 18th century was arguably quite marginal. Peter Gay's The Enlightenment: The Rise of Modern Paganism, unfortunately not mentioned by Greenblatt, deals at length with the influence of Lucretius on French Enlightenment thinkers, many of whom really were "pagans", i.e., materialists and epicureans. The standard view, of course, is that a revival of Platonic idealism, not of "pagan" materialism, was responsible for the Renaissance preoccupation with beauty and harmony.
Poggio's fifteenth century discovery of the manuscript of Lucretius's De rerum natura was not commented on much by Renaissance humanists, who confined themselves to remarks about Lucretius's grammar and syntax. It was printed in 1511 with a commentary by Denys Lambin, who termed Lucretius's Epicurean ideas "fanciful, absurd, and opposed to Christianity" -- and Lambin's preface remained standard until the nineteenth century. Epicurus's unacceptable doctrine that pleasure was the highest good, writes Jill Kraye, "ensured the unpopularity of his philosophy". See Jill Kraye's "Philologists and Philosophers" in the Cambridge Companion to Renaissance Humanism , p. 153-154.
If Renaissance Humanists such as Valla and Erasmus seemed to paradoxically endorse Epicureanism, it was in a Christianized and Platonized form in which love of God and life of virtue were seen as the highest pleasures. They certainly did not endorse Lucretius's materialism and they probably didn't even see the significance of his belief in atoms. Montaigne in his Essays, on the other hand, quotes Lucretius repeatedly, often without attribution, indicating that Lucretius's naturalism, if not his Epicureanism, was appealing to him.
In The Swerve, Greenblatt describes the fascinating 1989 identification of Montaigne's personal annotated copy of Lucretius. Greenblatt also cites Pietro Redondi's controversial portrayal of Gallileo as a closet materialist, while gliding hurriedly over the many objections that have been raised to Redondi's assertions. As a liberal and believer in science, myself, I fully sympathize with Greenblatt's predilections. He is a lively writer, but I think the public would have been better served by more balanced presentations, such as can be found, for example, in the writings of Anthony Grafton, who is especially good on humanism during transitional period between the Renaissance and the French Enlightenment. Grafton also traces the interrelationship of humanism and modern liberal ideas in a way that is attractive and convincing.