Correct, the Soviet counteroffensive started on Dec 5, 1941, two days before Pearl Harbor. History books note that it was completely ineffective for two days and largely ineffective for a number of days. Hitler signed Directive 39 on Dec 8th ordering the cessation of offensive operations. On December 11, Germany declared war on the USA and the USA, in turn, declared war on Germany.
The Soviet counteroffensive began to gather steam during this time. Some of Hitler's generals (Halder and Von Kluge) interpreted Directive 39, and perhaps because of the theoretical dicussion with Hitler about America as an enemy, that a general withdrawal to more defensible lines was warranted and provided the order.
On or around Dec 19, Hitler caught word about the withdrawal and forbade it. No doubt his fury was worsened by the reversal of Germany fortunes in the cold Soviet winter.
So I concede the point, albeit a minor point at that. It was the combination of delayed success in the Soviet counteroffensive, combined with the countermanding of his officers' orders, that hardened Hitler's mind about doing the reasonable and militarily correct thing.
I don't have a strong sense one way or the other but I have read German commander(s) grudgingly admit that Hitler's order to hold out at all cost prevented a bad situation from becoming an unmitigated disaster.