Fifty million is a minimum estimate for the population of the Roman Empire.  According to Lesley and Roy A. Adkins' Handbook to Life in Ancient Rome (1994):

"Most useful are the figures for totals of citizens registered under Augustus and Claudius.  These suggest that around AD 14 there were about 5 million free inhabitants of Italy, to which some demographic analysts conjecture that a population of 2 to 3 million slaves should be added.  Rome had a population of between 500,000 and 1 million, and other large cities had populations of 100,000 to 200,000.  Egypt seems to have had a total population of around 7 million. At the beginning of the 1st century, there is likely to have been a minimum of 50 million to 60 million people within the frontiers of the empire, possibly 100 million."  (p. 341)

Sorry to get pedantic (or even knowledgeable) on this issue, Eric, but I'd just been discussing this question on a mailing list and thought I'd share the information and quote.

Michael

Rather than just commenting on population figures, I thought I'd bring in a comment made on an alternate-history mailing list, based on the same Glenn Reynolds posting that you mention.  A member had proposed Rome might sooner have learned its lesson (communicated by Augustus in his famous advice to the future) about not expanding further.

Rather than Rome learning its lesson about the futility of further expansion earlier, I proposed that it never learned the lesson, or at least not till much later.  The question was suggested by a historically-minded reader's comments to Instapundit a few days ago (making some comparisons between modern American politics and the Roman), from whose letter I'll quote:

Mr. Lydon seems to assert that Hadrian's consolidation of the [Roman] Empire's borders and cessation of expansion was unquestionably beneficial.  But this interpretation is far from unassailable.

The Roman Empire was always at its strongest when it was on the offensive, pushing its borders ever further into barbarian territory and carrying the benefits of civilization with them, just as President Bush asserts that America can only triumph in the war on terror by staying on the offensive and bringing the fight to the enemy's heartland.  There's no reason to believe that the Democratic strategy of going on the defensive (by focusing on homeland security rather than regime change in hostile nations) will work any better for America than it did for Rome, which found it difficult to maintain static borders against the constant encroachments of barbarian tribes (again, just as our porous borders would be almost impossible to seal against terrorist infiltration).

In fact, it's arguable that Hadrian's reforms contributed to the eventual fall of the empire by sapping Rome of its drive and ambition for expansion, leading inevitably to decadence and decline.  It's hard to avoid drawing unfavorable parallels to Democratic pacifism and provincialism.

So, hopefully without impelling people to mix things up more with latter-day politics, what about the question of what would have happened if Augustus, say, had not bequeathed to his successors the advice of not advancing the borders further?  Suppose Augustus' recommendation had been to go ahead and advance the frontiers when feasible (after a war started by barbarian invasion, say, take their provinces into the Empire afterwards).  Or what if Hadrian had not reversed Trajan's gains?  What if Marcus Aurelius, say, after vanquishing the Germans of the upper Elbe and preparing to incorporate their lands as provinces, had not died suddenly in the midst of it all, and his lackadaisical son Commodus therefore did not have the opportunity to abandon all the Empire's painfully acquired gains?

Such advances need not have occurred very frequently; during the Republic it often took fifty years from one until the next new province was incorporated into the realm.  However, an established tradition of a policy of growth, not stasis, might have made a huge difference to the later history of the Empire.  Not only is there such a thing as historical momentum, which the Empire arguably abandoned in its satisfaction with holding the line, but had the Empire actually attained a stable Elbe-Danube frontier, or even better probably, Vistula-Danube frontier, the length of the borders requiring defense would have been considerably reduced, lessening the manpower needed to defend them and making the same number of defenders more effective.

I've also heard (haven't checked the details thoroughly) that a good portion of the military disaster of the mid-200's — when barbarian invasion devastated the West so thoroughly that it never recovered (Romano-Gaulish cities like modern cities had been unwalled heretofore and were almost totally destroyed) — can be attributed to the fact that the Roman army hadn't fought a real war for nearly a century, and thus was massively stultified and out of practice.  More frequent war-fighting experience might have made quite a difference there too.