The success of Operation Uranus (the Soviet counteroffensive which led to the encirclement and eventual destruction of the German Sixth Army at Stalingrad) wasn't as much a matter of the Germans "not seeing it coming" as much as it was that they just weren't able to stop it by that point. Intelligence failures and hubris on the part of the German commanders didn't help, but even if they had known the exact date and time of the attack, they probably couldn't have stopped it given the lack of available troops and materiel. They had overcommitted themselves months earlier and left themselves exposed to Soviet counterattacks, particularly on their flanks, and the Soviets took advantage of it.

The Battle of Stalingrad was part of the German summer offensive in southern Russia that began in late June 1942, known as Case Blue (Fall Blau). The plan was for Army Group South to strike through southern Russia into the Caucasus, securing vital oil production facilities near Maykop, Grozny, and Baku. The Germans desperately needed the oil supplies in these areas, since they had largely exhausted their strategic reserves and were depending on the Romanians and their own synthetic oil industry for their entire supply; Hitler famously said that "if I do not get the oil of Maykop and Grozny, then I will have to end the war". Army Group South was divided into two smaller Army Groups, A and B, for Case Blue. Army Group A would push south and carry out the offensive in southern Russia and the Caucasus, while Army Group B would push eastward to the Volga to protect the northern flank of Army Group A.

Army Group A initially made rapid progress, capturing the major city of Rostov-on-Don by the end of July and reaching Maykop by mid-August, only to find that the Soviets had carried out a successful scorched earth policy to deny the Germans the use of the oilfields there. The Axis forces met stiffer Soviet resistance as they pushed further south, and were unable to capture Grozny or advance into the Caucasus to take Baku, meaning that the Germans would have to survive the winter without that oil.

Army Group B obviously ran into even bigger problems further north. After the victory at Rostov, Hitler ordered Army Group B to take the city of Stalingrad itself, which he thought would secure the northern flank of Army Group South. Of course, this also meant a further commitment of precious resources, and was based on an underestimate of the Soviet strength in the area (and Hitler's own hubris about his strategic wisdom and the capabilities of the Red Army). Some historians (e.g. David Glantz) have gone as far as to say that the decision to capture the city was the turning point in the war, even before the battle itself, and considering the outcome, it's hard to disagree.

It took about six weeks of difficult fighting, including a significant battle at Kalach-on-Don in late July, for Army Group B to advance from Rostov to Stalingrad, which further drained the German forces before they even reached the city. Once the Germans entered Stalingrad on 12 September, they became bogged down in grueling house-to-house fighting, as the Soviets were ordered to hold the city at all costs. Both sides endured massive casualties in this slow, close-quarters fighting, which was part of the Soviets' tactics, intended to negate the Germans' advantages in maneuverability and the fact that the Luftwaffe had air supremacy over the city from the early days of the battle, complicating Soviet efforts to reinforce their troops, since they had to cross the Volga River to do so, leaving them exposed to German aircraft. It took the Germans until mid-November to reach the Volga River, by which point they had secured most of the city, but at the expense of tens of thousands of casualties for the Sixth Army.

The Achilles' heel of the German position was their flanks outside the city. The Germans decided to leave the coverage of their flanks to their allies, mainly Romanian, Hungarian, and Italian troops. These units were poorly-equipped and poorly-trained, and weren't going to hold up against a strong Soviet offensive. The Germans didn't give them much in the way of reinforcements (no more than a couple of divisions), and their positions weren't well-defended, since the Germans had been focused on taking Stalingrad, not on consolidating their lines along the Volga. This meant that the German flanks were badly exposed.

Obviously, the Soviets knew this. They realized the Germans were overextended and that the Romanian Third and Fourth Armies, which were defending the northern and southern flanks of the Sixth Army, respectively, didn't have the equipment or training to contend with a concerted Soviet counterattack. The Soviet buildups were reported by the front line commanders, but the German High Command wasn't concerned, since they knew the Soviets were also building up forces further north, opposite Army Group Center near Rzhev, and believed that the Soviets were incapable of carrying out two simultaneous offensives on different parts of the front. They were obviously wrong, since a few days after the Soviets launched Operation Uranus, they launched Operation Mars, which was intended to encircle the German Ninth Army in the Rzhev salient, although the Germans successfully fended off that attack.

As I said before though, even if the Germans had had perfect intelligence on the Soviet strength and a realistic assessment of the Soviet plans, they probably couldn't have done much to stop Uranus. The Two Romanian Armies were defending a combined front line area of over 200 miles (in places, the Romanians had about 50 men per mile of front), and most of their equipment was obsolete, meaning they had little chance of resisting the modern Soviet mechanized forces. The Germans compounded this problem by transferring some of their mechanized units to the Western Front, leaving their forces near Stalingrad even more exposed. The Fourth Panzer Army was the only German formation that was capable of protecting the rear of the Sixth Army if the Soviets managed to break through the Romanians on the flanks.

When the Soviets launched Operation Uranus on 19 November, they had over 1.1 million men committed to the offensive, while the Axis had about 400,000 German and Romanian forces in the immediate vicinity of the Soviet attack. The Romanian forces on the German flanks were completely routed within the first two days of the offensive, and the Germans weren't able to react quickly enough or with sufficient strength to prevent the encirclement of most of their troops at Stalingrad by 23 November, including most of the Sixth Army, part of the Fourth Panzer Army, and the remainder of the Romanian Third and Fourth Armies, a total of over a quarter of a million men.

Hitler, of course, ordered the Sixth Army not to attempt a breakout, instead choosing to supply them by air while forces outside of the encirclement attempted to break through the Soviet lines along the Don River. The German offensive, known as Operation Winter Storm, was carried out by the underequipped remnants of the Fourth Panzer Army and the Romanian Third Army, Predictably, this offensive failed, and the Soviets launched a counteroffensive, Operation Little Saturn, which forced the Germans back across the Don and led to further encirclements (notably the Hungarian Second Army near Voronezh), although it failed to achieve its overall objective of trapping Army Group A in the Caucasus. After the failure of Winter Storm, the fate of the Sixth Army was essentially sealed. At that point, they couldn't have attempted a breakout even if Hitler allowed it because their forces were too weakened and too short of supplies.

So essentially, the Germans had sowed the seeds of their own demise well before the Soviet counteroffensive at Stalingrad even began. Their commitment to capturing the city, and the cost of the resulting urban warfare, left them short of men and materiel and reliant on their insufficiently equipped and overstretched allies for the defense of their flanks. Those units had no hope of resisting a Soviet mechanized offensive, and the Germans weren't capable of reinforcing them to a point where they could have prevented Operation Uranus from succeeding.

The moral of the story, kids, is always watch your flanks, because they can be your downfall (and also, Russia is really big and invading it will invariably overstretch your forces, so don't).

Sources

Mark Axworthy, Cornel Scafeș, and Cristian Crăciunoiu, Third Axis, Fourth Ally: Romanian Armed Forces in the European War, 1941-1945 (Arms & Armour, 1995)

Anthony Beevor, Stalingrad (Viking, 2004)

David Glantz and Jonathan House, When Titans Clashed: How the Red Army Stopped Hitler (UP of Kansas, 1995)

Ian Kershaw, Hitler, 1936-1945: Nemesis (Penguin, 2000)