Would they have moved their administration/capital to the East? In the event of Moscow's fall, what would Germany have done: continued into Siberia or negotiated a peace treaty?
In October 1941 the Soviets began seriously discussing the possibility of Moscow falling. Stalin decided that he was going to stay in the capital. It was feared that seeing Josef Stalin and the government flee would cause a massive panic among the cities massive population. There was also an idea of burning Moscow similar to what the Russians had done to Napoleon. But Stalin saw that when Moscow was burned in 1812 it was little more than a small town, the Moscow of 1941 was a vast, sprawling modern city.
Stalin also used this new boost of energy to begin taking control of the situation. The new stet defence committee began to make preparations for defending against the Germans, and on October 10th, stalin appointed Georgia Zhukov to defend the capital. Stalin said that there would be "no evacuation" and than he said that "We'll stay here until victory".
Even with Stalin's assurances some sectors of the city began to delve into panic and mass hysteria. However Zhukov got a handle on the situation and declared martial law. He had over a million men to defend the city. It was assumed that the Germans would try and encircle the city, so a massive amount of conscript troops were placed behind the city on the Volga river, Stalin as Zhukov both hoped this would stop the encircle men of the city.
In all likely hood had it looked like the Germans were going to take Moscow, the majority of the soviet government would have probably fled east and continued the fight. Stalin might have as well. But the prospects looked good for the soviets, they had a superior amount of men, equipment, and were equipped for winter fighting. Stalin had no reason to panic.