The NPR article describes two strategies:
1. culling - reject large categories of items as not worth consuming
2. surrender - acknowledge that time is finite and one just won't get to some items which are (nevertheless) worth consuming
As The League and some of his commenters pointed out, in practice most people utilize both strategies, and both indeed seem necessary in this era of information oversaturation. But it still leaves the question of whether or not it is still possible to be "well read," and if so, what that would mean. The suggestion of the NPR writer seems to miss the point of the original phrase.
If "well-read" means "not missing anything," then nobody has a chance. If "well-read" means "making a genuine effort to explore thoughtfully," then yes, we can all be well-read. But what we've seen is always going to be a very small cup dipped out of a very big ocean, and turning your back on the ocean to stare into the cup can't change that.
"Well read" when said of Thomas Jefferson (The League's example) or David Foster Wallace, or a witty conversationalist one meets at a cocktail party certainly does not mean "not missing anything." And "making a genuine effort to explore thoughtfully" doesn't seem very helpful for those who wish to be "well read."
A natural way to interpret the phrase is in terms of a list of must reads, works anyone must have read in order to be "well read"—as The League points out, however, if this list is identified with the canon as taught in high school, it seems problematic. How was it chosen? Why Thomas Hardy, whom every schoolboy hates?
If custom, or even whim, dictates some of the members of the high school English class canon, how can we separate out the wheat from the chaff? I think there is definitely a unique set of problems which arise post-20th century for this endeavor.
1. Maybe sufficient longevity of popularity is enough to ensure the read-worthiness of some works (e.g. The Iliad or Shakespeare), but this process is open to artificial corruption (e.g. continued "popularity" of Thomas Hardy as measured in sales of books to students for whom it is required), requires culling itself (e.g. must one today have read Caesar's Gallic Wars to be well read? Even if that might have been the case 200 years ago in England?), and, perhaps most importantly, does not apply to contemporary works which one must read to be "well read."
Strangely, Ebert's musings are set off by reminiscing about authors considered required reading in the mid-20th century, but whom have become forgotten, irrelevant, or both:
"Consider: who at this hour (apart from some professorial specialist currying his "field") is reading Mary McCarthy, James T. Farrell, John Berryman, Allan Bloom, Irving Howe, Alfred Kazin, Edmund Wilson, Anne Sexton, Alice Adams, Robert Lowell, Grace Paley, Owen Barfield, Stanley Elkin, Robert Penn Warren, Norman Mailer, Leslie Fiedler, R.P. Blackmur, Paul Goodman, Susan Sontag, Lillian Hellman, John Crowe Ransom, Stephen Spender, Daniel Fuchs, Hugh Kenner, Seymour Krim, J.F. Powers, Allen Ginsberg, Philip Rahv, Jack Richardson, John Auerbach, Harvey Swados--or Trilling himself?" [Ebert quotes Ozick]
But this brings us to:
2. Being "well read" seems context specific. Certainly, temporally context specific—if Ebert's discussion is presumed to be relevant, than a greater onus falls upon he who would be "well read" to pursue the top works of his own time, than those of the past. Or, to put it in the above terminology, his culling of contemporary works is assumed to be less severe.
Also, here, one might want to add cultural or geographic context specificity. Can the "well read" Englishman and the "well read" Spaniard be expected to read the same (or even largely the same) books? Surely one is to read Shakespeare in the original and the other to read Cervantes. But in an age of increasing informational contact between cultures, how much from outside and how much from within is the "well read" supposed to consume? Am I expected to read every Nobel Prize winner? Has anyone? What if their works have not been translated into my language? And also here, one must temper the value of such works by the cost of translation: a lesser work by a writer of one's native language may have a greater positive effect in improving one's rhetorical and linguistic skills (marks of the "well read"?) than a superior work translated from the original.
3. The problems of media and genre. The League rightfully defends the value of cultivating genre interests. Part of the benefit of being "well read" comes in uncovering layers of meaning in new works, of spotting allusions, of recognizing influences and references, of fully understanding the language they use—yet this endeavor seems possible today only within a narrowly defined genre / medium. Although I cannot grasp all the languages in communicative use today, I may be able to grasp the language of film, of poetry, of comics, of the mystery novel, the sci-fi novel, the pot-boiler, or some other one or handfull of the myriad niche markets which have arisen.
As the amount of available information increases, inevitably, the expected overlap in background knowledge diminishes. While a British novelist in the nineteenth century might have been able to assume a broad familiarity with Shakespeare and Chaucer and major Latin works amongst his readers (hmm, here also contextualization by class?), the modern writer can make no such assumptions. Within the confines of genre, however, expectations are heightened. If you would only be reading this piece were you a fan already, and being a fan implies reading such and such other pieces, then the writer / creator can assume you've read them, and reference them and build on them. Ideally, heightening the complexity of their work (and also your enjoyment of it). Not that things always work out this way.
I think these worries speak against the possibility of a list of canonical works for the "well read." I don't think this defeats the possibility of being "well read," though. To me, the word refers to one who has read widely, but also has digested and internalized the information he consumed. There must be a familiarity with classics, particularly those which shaped modern thought and language (Shakespeare on every list here). In terms of contemporary works, allowances for culling must be made. I would not withhold the term "well read" from someone just because they had not read (say) David Foster Wallace's Infinite Jest, even though that work is superior to most of those on Ebert's list. It's simply too much to expect.
Perhaps, though, the bottom line is just that to be "well read" is no longer meaningful. One could read the works that made one "well read" once upon a time, yet not achieve the same effect—understanding the context of every remark, catching every reference, spotting and understanding every allusion. And no alternative strategy seems able to achieve that effect either.