This is very hard to put a firm date to (actually, its impossible), but I can say with some confidence the 1943 address was NOT when an overwhelming realization swept the German population, though it did begin to plant seeds of doubt; and here's why...

The Sportspalast speech was delivered to a highly selective audience, and was therefore received to deafening roars of approval. The long story short of that speech was the announcement of a total war ideology, which the Allies had already been following for quite some time, one must note. One of its fundamental messages was 'we have only just started.'

The Wehrmact's aura of invincibility was shattered for the military and political elite at Stalingrad, but the public was kept largely in the dark. Those who were aware might not have been too concerned, it was, after all, their first major land defeat of WWII, and civilians and the average citizen would not have realized the shocking implications it would've had for the German's combat effectiveness - especially when we factor in the propaganda mill; it was simply something to bounce back from (again, the overall message of the Sportpalast address).

For some Germans, even the ones who suffered and were captured in that major defeat, didn't fully realize the gravity of the situation following Stalingrad. I quote:

[Some prisoners], still dreaming of great counter-attacks which would free them, became convinced at night that they could hear the guns of the advancing army (Beevor, p. 420)

Higher up, a sense of betrayal permeated the General ranks of those captured in Stalingrad, and abortive attempts to turn them into communist agitators were made:

On 19 August, 1943, three [Sixth Army] Generals, Seydlitz, Lattmann and Korfes, who had been identified from interrogations as likely collaborators, were taken....to a 're-education center' at Lunovo....(p. 421)

This attempt would be led by Seydlitz, who became outraged at what he viewed as a morally bankrupt regime led by Adolph Hitler, but Soviet mistrust of the German's intentions (quite rightly) halted anything from materializing from this 'League of German officers.' Naturally, while a propaganda coup in the Soviet Union itself, none of this had any true affect on the German home front. Hitler's reaction to this change of heart was swift, and he summoned notable German generals to openly condemn Seydlitz. With national heroes like Rommel and Manstein part of this reaction, the average German citizen would've been reassured, I think its safe to say.

Earlier in the book 'Stalingrad', Beevor elaborates on what I've lightly mentioned:

Presenting such a catastrophe to the German people was a challenge to which Goebbels had risen with frenetic energy...the regime had not admitted that the Sixth Army was encircled until 16th January....now, it chose entirely the opposite direction, claiming that not a single man had survived. (p.398-399)

By turning the German people's sorrow into anger and hatred, and making martyrs out of the 6th Army at Stalingrad, the regime effectively delayed the realization that something was horribly amiss, and deluded the implications of the events beyond repair. Goebbels effectively replaced a sense of dread with a sense of defiance, tying it in neatly to the self-created mythos of the Nazi state. A period of national mourning was organized, and any and all signs of sorrow closely monitored and controlled by the regime. Final letters from Stalingrad were destroyed or hidden from the public so that they would not contradict the story of dying to the last man, and civilian morale was therefore tightly monitored. Was there shock? Yes, absolutely, how could there not be after such a stunning defeat, did civilians connect the dots? Not as much as they should have.

So, to answer your question, I doubt highly it hit the German people after the 1943 address. Indeed, for many citizens, it would not hit until there were Allies fighting within their country itself. If I had to hazard an educated guess, the German people began to realize the war was lost when setbacks were undeniably transforming into a string of defeats; when the homeland could no longer be protected by its own air force, when it was clear the Germans were in retreat on all fronts. In other words - when the regime could no longer dismiss defeats in battle as anomalous or temporary setbacks.

Edit: Grammar, syntax, etc.

Although the answer is somewhat subjective (how does one quantify public opinion is a major dilemma for social history), the best answer was just after the loss of Stalingrad (early 1943). There was a growing unease with the inability of German armies to wrestle a complete victory in 1941 and 1942, and Stalingrad confirmed these suspicions. This is from an earlier answer of mine on a similiar topic:

About one third of the German population realized the war was lost in late 1942 and early 1943 according to US Strategic Bombing Surveys conducted in1945. The Battle of Stalingrad was an essential catalyst for this shift in public opinion. One Augsburg individual said "The Führer has also spoken himself about how important Stalingrad is, and now he has gone and lost it."

It's also important to realize that Stalingrad was only one of several major reverses (losses in North Africa and the increasing presence of Allied bombers). What was rapidly becoming clear to many Germans was that the war was not going to be brought to a rapid conclusion and the tide had shifted against Germany. SD reports indicated that Stalingrad acted as a symbol for Germany's wider fortunes, and created "a general feeling of deep shock" and that there "there is a general conviction that Stalingrad signifies a general turning point in the war."

Sources

Evans, Richard J. The Third Reich at War. New York: Penguin Press, 2009.

Kershaw, Ian. The "Hitler Myth": Image and Reality in the Third Reich. Oxford: Clarendon Press, 1987.