I would argue that Sauron did likely have a total military strength in the millions, consisting of the forces of Mordor and all his allies and vassals in the East. Sauron had spent centuries building his forces and all the civilized world except for the northwest of Middle-Earth was to some greater or lesser degree under the sway of Sauron.

Remember at the Siege of Minas Tirith and the Battle of Pelennor Fields, Sauron was hugely, catastrophically unlucky. It's almost as if God himself was plotting against in as part of some grand scheme.

1. Sauron had to fire off the campaign earlier than expected, instead of carrying everything out according to plan, because Aragorn used the palantir to convince him that Aragorn was in possession of the One Ring, which was Sauron's only weakness.

‘Ere that dark day ended none of the enemy were left to resist us; all were drowned, or were flying south in the hope to find their own lands upon foot. Strange and wonderful I thought it that the designs of Mordor should be overthrown by such wraiths of fear and darkness. With its own weapons was it worsted! ’

3. The Rohirrim, instead of being cut off by the numerically vastly superior forces between them and Minas Tirith, are guided down secret paths by forgotten forest-men that bear an ancient grudge against both Sauron and regular Men.
4. What do you know, the very weatherl, which was supposed to be under his control, conspires against Sauron, turning back his Great Darkness earlier than planned.

So consider the situation if any one of these unforseeable factors had not occurred: Sauron successfully takes a extremely well-fortified city, which has been preparing for a siege for months, in two days. Clearly the force attacking Minas Tirith alone was vastly numerically superior to even the combined armies of Rohan and Minas Tirith, and very well-equipped for siege warfare. I think it's not unreasonable to expect that the force assaulting Minas Tirith, guarding the road, and pillaging the surrounding area outnumbered them by at around 10x, giving us a force somewhere in the 100ks.

But this was not the only active army in the field. Sauron's forces were at the same time assaulting South Gondor, Mirkwood, Lothlorien, Dale, and Erebor. In these cases too, Sauron seemed to be relying on overwhelming force and well-equipped troops.

Tor my part I heeded them not,’ said Gimli; ‘for we came then at last upon battle in earnest. There at Pelargir lay the main fleet of Umbar, fifty great ships and smaller vessels beyond count. Many of those that we pursued had reached the havens before us, and brought their fear with them; and some of the ships had put off, seeking to escape down the River or to reach the far shore; and many of the smaller craft were ablaze. But the Haradrim, being now driven to the brink, turned at bay, and they were fierce in despair; and they laughed when they looked on us, for they were a great army still.

Lorien seems to have held thanks to the power of Galadriel, who only Sauron could have defeated:

So, if not for totally unforeseen events, Sauron would have won a crushing victory in just a few days. His only enemies even halfway capable of projecting force would have been defeated, Erebor would have been besieged, and he could have reinforced the armies attacking Mirkwood and Lothlorien at his leisure. He didn't need any bigger armies than what he had.

To this City only the first finger of its hand has yet been stretched. All the East is moving.

(Denethor, in The Pyre of Denethor)

Nonetheless it cannot be doubted that when Denethor saw great forces arrayed against him in Mordor, and more still being gathered, he saw that which truly is.

‘Hardly has our strength sufficed to beat off the first great assault. The next will be greater. This war then is without final hope, as Denethor perceived. Victory cannot be achieved by arms, whether you sit here to endure siege after siege, or march out to be overwhelmed beyond the River. You have only a choice of evils; and prudence would counsel you to strengthen such strong places as you have, and there await the onset; for so shall the time before your end be made a little longer.’  (Gandalf, in the Last Debate)

Gandalf's words reaffirm for us that Sauron's armies did not just outnumber the free peoples of Middle-Earth, there wasn't even a contest, a hope of victory. Smaller armies defeat larger armies all the time! This is especially true in defensive and siege situations. They definitely don't fall in a few days! Consider the Siege of Constantinople, for instance - a very well fortified city, drastically undermanned, the defenders outnumbered 10 to 1, facing new cannon technology that made their invincible walls slightly less invincible. They held out for 53 days.

...and that Sauron had spent centuries preparing for this war, mostly by getting the East together, and the past 67 years openly doing preparing for war. But again, Sauron did not need much more than he had in the field: at Minas Tirith he was badly unluckly, at Mirkwood he apparently suffered a hard-fought defeat, and everywhere else he was victorious, and he had troops in reserve to send out and deal with it.

I would argue that Sauron did likely have a total military strength in the millions, consisting of the forces of Mordor and all his allies and vassals in the East. Sauron had spent centuries building his forces and all the civilized world except for the northwest of Middle-earth was to some greater or lesser degree under the sway of Sauron.

Remember at the Siege of Minas Tirith and the Battle of Pelennor Fields, Sauron was hugely, catastrophically unlucky. It's almost as if God himself was plotting against him as part of some grand scheme.

1. Sauron had to fire off the campaign earlier than expected, instead of carrying everything out according to plan, because Aragorn used the palantír to convince him that Aragorn was in possession of the One Ring, which was Sauron's only weakness.

‘Ere that dark day ended none of the enemy were left to resist us; all were drowned, or were flying south in the hope to find their own lands upon foot. Strange and wonderful I thought it that the designs of Mordor should be overthrown by such wraiths of fear and darkness. With its own weapons was it worsted!’

3. The Rohirrim, instead of being cut off by the numerically vastly superior forces between them and Minas Tirith, are guided down secret paths by forgotten forest-men that bear an ancient grudge against both Sauron and regular Men.
4. What do you know, the very weather, which was supposed to be under his control, conspires against Sauron, turning back his Great Darkness earlier than planned.

So consider the situation if any one of these unforeseeable factors had not occurred: Sauron successfully takes a extremely well-fortified city, which has been preparing for a siege for months, in two days. Clearly the force attacking Minas Tirith alone was vastly numerically superior to even the combined armies of Rohan and Minas Tirith, and very well-equipped for siege warfare. I think it's not unreasonable to expect that the force assaulting Minas Tirith, guarding the road, and pillaging the surrounding area outnumbered them by at around 10x, giving us a force somewhere in the 100ks.

But this was not the only active army in the field. Sauron's forces were at the same time assaulting South Gondor, Mirkwood, Lothlórien, Dale, and Erebor. In these cases too, Sauron seemed to be relying on overwhelming force and well-equipped troops.

‘For my part I heeded them not,’ said Gimli; ‘for we came then at last upon battle in earnest. There at Pelargir lay the main fleet of Umbar, fifty great ships and smaller vessels beyond count. Many of those that we pursued had reached the havens before us, and brought their fear with them; and some of the ships had put off, seeking to escape down the River or to reach the far shore; and many of the smaller craft were ablaze. But the Haradrim, being now driven to the brink, turned at bay, and they were fierce in despair; and they laughed when they looked on us, for they were a great army still.

Lórien seems to have held thanks to the power of Galadriel, who only Sauron could have defeated:

So, if not for totally unforeseen events, Sauron would have won a crushing victory in just a few days. His only enemies even halfway capable of projecting force would have been defeated, Erebor would have been besieged, and he could have reinforced the armies attacking Mirkwood and Lothlórien at his leisure. He didn't need any bigger armies than what he had.

To this City only the first finger of its hand has yet been stretched. All the East is moving.

(Denethor, in "The Pyre of Denethor")

Nonetheless it cannot be doubted that when Denethor saw great forces arrayed against him in Mordor, and more still being gathered, he saw that which truly is.

‘Hardly has our strength sufficed to beat off the first great assault. The next will be greater. This war then is without final hope, as Denethor perceived. Victory cannot be achieved by arms, whether you sit here to endure siege after siege, or march out to be overwhelmed beyond the River. You have only a choice of evils; and prudence would counsel you to strengthen such strong places as you have, and there await the onset; for so shall the time before your end be made a little longer.’ 

(Gandalf, in "The Last Debate")

Gandalf's words reaffirm for us that Sauron's armies did not just outnumber the free peoples of Middle-earth, there wasn't even a contest, a hope of victory. Smaller armies defeat larger armies all the time! This is especially true in defensive and siege situations. They definitely don't fall in a few days! Consider the Siege of Constantinople, for instance - a very well fortified city, drastically undermanned, the defenders outnumbered 10 to 1, facing new cannon technology that made their invincible walls slightly less invincible. They held out for 53 days.

...and that Sauron had spent centuries preparing for this war, mostly by getting the East together, and the past 67 years openly doing preparing for war. But again, Sauron did not need much more than he had in the field: at Minas Tirith he was badly unlucky, at Mirkwood he apparently suffered a hard-fought defeat, and everywhere else he was victorious, and he had troops in reserve to send out and deal with it.