Germany wasn't "still busy" fighting Great Britain at the time.
The conflict against the GB was never really likely to develop onto a full-scale battle as Germany lacked the basic resources to attack mainland GB.
Hitler had no landing craft, the "Rhine barges" that have often been mentioned a being possibly used as landing craft would have been hopeless in such a situation as they would have capsized in anything but the calmest of waters.
The Royal Navy was also far too strong for the Kriegsmarine to have afforded any lasting protection to such landing forces, while they may have managed to land on the beaches of southern England they would not have been able to maintain naval supremacy to allow reinforcements or supplies to arrive in the coming days.
Even had the Luftwaffe managed to subdue the Royal Air Force, a feat that they came fairly close to achieving, this would have had little effect on sea actions. It's been well documented how bad the Luftwaffe were at engaging warships, look at how little damage they did to British forces evacuating at Dunkirk for example. Dunkirk was a good trial run for the Luftwaffe to see how they would fair against the Royal Navy and yet they had extremely poor results against ships that were often sitting ducks, not moving but tied up to the harbour wall while the troops embarked.
Hitler's last desperate gamble in changing the focus of the attack from the Royal Air Force and onto the cities was a vain attempt to get Britain to surrender or at least sue for peace.
So Hitler knew he had to attack Russia, before Russia attacked Germany. Britain at this time was not a major problem to Germany, Hitler knew they couldn't mount any serious opposition other than a few air-raids and even those were limited to night attacks as the Luftwaffe could mount a good defence of mainland Europe in those days.
The Russian Army was in a terrible state at the start of the war due to Stalin's purges where many of his best commanders were executed or sent to the Gulags in Siberia for not being Communist enough, to paraphrase.
Their armed forces were generally badly trained and equipped too, while the T34 was available it was only in small numbers and they had only a few modern aircraft and the ones they did have generally did not have trained pilots to fly them
Arguably Hitler should have attacked even sooner, but he got bogged down helping the Italians in the Balkans conflicts and so Barbarossa did not start until June 1941, a month or so earlier might have made a big difference to the outcome.
So, the reality is that the Germans weren't actually fighting on two fronts as the war with Great Britain was limited to the Luftwaffe providing air-defence of the Reich. Most of the troops deployed to defend the coastline were poor quality conscripts and even prisoners.