With possession of the entire North African coast, the US will push for a cross Channel invasion in Spring/Summer 1943. That might be disastrous except that Hitler will likely still strip the rest of Europe for his Kursk offensive.
If the US is smart, they won't invade until Hitler commits his forces at Kursk. That will prevent any quick reinforcements to the West. By the time Hitler is able to do that, the Western Allies should not only have a secure bridgehead, but pushed substantially inland. Without a certain incident in Sicily, Patton is likely to be one of the original commanders, perhaps even an Army Group leader.
The German counterattack is likely to be devastating, but I don't think they'll succeed in pushing the Allies back across the Channel. The Allies may even recover lost ground before 1943 ends. Hard to say where the final battle lines will be drawn for that year. So much depends on specifics.
If the Allies invade before Germans attack Kursk, things get a lot uglier as Hitler may cancel the attack and throw the resources into France. Of course, Hitler may decided on an entirely different strategy with such a quick conquest in North Africa.
Of course, the British might succeed in cancelling any such plans. They were very reluctant to cross the Channel. But it's hard to see how they can win that fight if the US argues hard and the landing craft resources are available.