Germany’s prewar population was 69 million, as opposed to 169 million for the Soviet Union. It’s also worth bearing in mind that the Soviet Union expanded after the war began; and that many people in Soviet-occupied territories were coerced into fighting for the Soviet Union. For example, the Soviets convinced the people of Soviet-occupied east Poland to fight for them, by threatening to liquidate the family of any man who refused to fight. That didn’t necessarily result in very effective soldiers, but it swelled the Soviets’ numbers over and above what you’d expect from that 169 million. Germany added territory as well, but unlike the Soviets, it did not use coercion to force captured foreign populations to fight for it.
Neither the Soviet Union nor Germany could afford to devote its sole attention to the other. The Soviet Union had soldiers tied down near its border with Manchuria, to guard against a Japanese attack. (Most of those soldiers were released for duty on the Soviets’ western front after Pearl Harbor.) Germany had large forces tied down in Norway, France, and north Africa, to guard against the possibility of British (and later American) invasion. The Soviet Union could devote a greater portion of its military strength to Germany, than Germany could to the Soviet Union.
During 1942, the Soviets produced nearly twice as many military aircraft as Germany–not to mention the large numbers of planes they received through Lend-Lease. During 1942, the Soviets produced 3 - 4 times as much as Germany in nearly every major land weapons category (such as tanks and artillery). In 1942, Soviet tanks (such as the T-34) were better than their German counterparts. From 1941 until near the end of the war, the Red Army added men at the astounding rate of 500,000 per month. Germany could not come remotely close to matching that rate. By the summer of 1941, 80% of German men between the ages of 20 and 30 were already part of the German military. The other 20% performed vital industrial functions. Due to the Soviets’ far greater capacity to replenish losses, they were better positioned to win a long war than Germany.
In spring of 1941 the German Army consisted of 150 divisions–100 of which were used to invade the Soviet Union. In late '41 the Red Army’s size peaked at 600 divisions. Losses on the German front would later reduce that army to 450 divisions. It was more or less able to maintain a 450 division army for the rest of the war–using its 500,000 men/month recruiting to offset the men lost to Germany. While a Soviet division was somewhat smaller than a German division, those numbers nevertheless illustrate the numerical superiority the Soviets enjoyed.
A typical German soldier was about three times as combat-effective as his Soviet counterpart. It’s also worth noting that of the top 100 flying aces during WWII, all 100 came from Germany. The skill of German pilots allowed Germany to maintain air superiority on its eastern front in 1942, despite the production numbers I just mentioned. The Soviets did not achieve air superiority until (IIRC) 1944.
Despite the effectiveness of German infantry and German pilots, the overall strategic situation clearly favored the Soviet Union in 1942. However, there was an element of risk. The Soviets derived 80% of their oil from the Caucasus oilfields. If all of those oilfields were destroyed or conquered by Germany, a lack of oil would significantly alter the Soviets’ overall war effort. Of course, they could still achieve something with that remaining 20%. Also the United States had plenty of oil, and could have sent some of it to the Soviet Union. The loss of the Caucasus oilfields would not necessarily have been fatal to the Soviets’ war efforts. (Though the acquisition of those oilfields would have helped Germany solve its own oil-related problems.)
Suppose, for the sake of argument, that the Germans had succeeded in their objective of breaking through to von Paulus’s 6th Army at Stalingrad. Simply saving the 6th Army would have been a far, far cry from conquering all the Caucasus and its oilfields. The Caucasus is a vast area. The vast majority of the Caucasus area would have been unconquered, even if the Germans had gained complete control over everything within a 20 mile (~30 km) radius of Stalingrad.
The German summer offensive of 1942 had initially produced impressive gains. Stalin had expected the Germans to strike against Moscow, and has positioned the bulk of his forces in the center to guard against such an attack. Instead the Germans attacked in the south. But after the Soviets figured out what was going on, they transferred large forces south. Those forces would have been sufficient to prevent additional large German gains, even if the Germans had simply bypassed Stalingrad. Even if the Germans had captured some of the Caucasus oilfields, they had lost the chance to capture the entire Caucasus oil-producing region. (Assuming, of course, that there had ever been such a chance.) It is for these reasons that I do not see Stalingrad as a last stand. However, WWII was the largest and most important war in human history; and a case could be made that Stalingrad was the most important battle of that war. The Axis suffered 850,000 men killed, wounded, or captured during Stalingrad, as opposed to 1.1 million men for the Soviet Union. Given that Germany initially invaded the Soviet Union with only about 3 million men, Stalingrad represented a serious alteration in the strength of the German Army.