If they had succeeded in assassinating Hitler but did it earlier on and stopped the genocide things could have gone a lot smoother in the long run. Churchill wanted peace but knew that Hitler wouldn't stop which is why Britain continuously denied peace claims. Eventually (if Germans hadn't fought at Stalingrad and went straight for Moscow upon realizing where the Russians were placing so many troops), Stalin may have died in the upcoming battle if he didn't leave. The USSR would be in shambles and would eventually surrender. Without the death camps the Russian populace would have been left alone and just aided in the reconstruction. If this happened a war against the UK and U.S. would have been a stalemate unless a miracle happened.
My god... the regurgitation of so many myths about the Nazi war effort and the German high command... it's downright painful.
The real answer to the OP is that the war either doesn't start, or goes worse for Germany.
While the orthodox view of the German officer class was that Germany would have to regain her power and position through offensive war against her neighbors, they dissented greatly on the specifics - namely, the "when." OKW wanted to delay war until some time around 1945/46 when they felt they'd be fully prepared.
Hitler called them a bunch of old women with no strategic insight, and overrode them. And he was right. What OKH had failed to realize was that Germany had stolen a march on the Allies with early re-armament, but France and Britain were catching up rapidly, while Germany's stocks of strategic resources, and her ability to sustain high rates of production was beginning to fall. By 1946 the military balance would have grossly favored the Allies. If it was to be war, Hitler had to strike fast while he still had the advantage.
The problem is that Rommel lacks both Hitler's strategic insight and his personal power. In 1939 he was just another general, and not a particularly senior one. In Poland he impressed Hitler greatly with his command of the Fuhrer's HQ, enough that he was granted a Panzer division for the Battle of France, but right now he lacks any personal authority over either the Wehrmacht OR the Nazi Party. Over the past several years, Hitler had created a system that was loyal to him alone and Rommel simply doesn't have the reputation or the contacts to slide into that and take over.
Chances are he dies in fairly short order to assassins sent by Himmler or Goering, or faces willful insubordination from the military itself which considers him an arrogant upstart and grossly undermines the war effort - if it even starts on schedule. The High Command may revert to demanding a longer period of build up, and Rommel will lack both the power and the insight to decisively overrule them. Accepting their favored timeline may well be Rommel's price for their support against Nazi Party backstabbing.
All in all, it'll create a total mess for Germany, and probably badly undermine their war effort. So a Germany under Rommel probably won't invade the Soviet Union but then it probably won't be able to defeat the British and French either.