If Hitler had chosen not to attack while facing Britain in the West, he'd probably have done so after some peace agreement had been reached. Hitler, and the Nazis in general, always thought of Eastern Europe as Germany's "vital space" or Lebensraum, from which to harvest food, raw materials and slave labor. It was also Hitler's lifelong dream to eradicate bolschevism, so we can be sure that sooner or later he would have made the decision to attack the USSR.
On the other side of the border, the Soviet were not up for peaceful cohexistance either. Sure, they had and important trade partnership with the Reich: they traded oil, grains and other raw material for german machinery and designs; actually, the German war machine would have run out of essential supplies were it not for such trade. But Hitler had never made it a secret that he believe the Reich's right to dominate Eastern Europe and its inferior peoples. Nor were german divisions stationed on the shared border a sign of trust.
Others have speculated that if the USSR was to launch an attack on Germany, the Reich would have quickly fallen to the soviets. I don't think so. During operation Barbarossa, the German war machine was defeated by three fatal errors: the skizophreny of the German High Command, a serious underestimation of soviet potential, and strategic choices regarding the composition and deployment of armored divisions. Nontheless, the Wermacht was able to push the russians back to Moscow, inflicting upon them heavy casualties and chatastrophic loss of land, especially agricultural land in Ukrain. All that, with outstretched supply lines and an extremely primitive transportation system, as many have pointed out.
Imagine Germany fighting the same war, only with much shorter supply lines and a background of railroads and decently paved roads, and without the Russian winter. Add to that the morale boost from fighting in defense of the Fatherland against the communist invader. The Soviet potential might have crushed the Reich, but not as quickly and easily as some have speculated.