Yes, but not for the want of trying by the Americans. Who, wanted to land as soon as possible e.g. 1942. It seemed the was a running battle with the British over when it would be. The British wanted to spread the Germans about with diversions, so they wouldn't know where the next threat would really be, whilst the US seem to view that as mere distraction from having the major campaign in western Europe.An Allied invasion of mainland Europe in 1942 was ruled out because the Allies were simply not ready. They lacked the forces and the skills required.
Hence, French North-Africa happened as a way of using US troops against the Germans in '42. It had been planned for earlier, with the expectation the the 8th Army would be almost on the Tunisian border, but shelved, to resurrected later. The Campaign, had the added bonus of bring France back into the war, with their additional troops.
Once the African shore of the Med had been cleared, to ensure safety of shipping Sicilly had to be taken. The US still thought, it was being diverted from a '43 D-Day - hence any reluctance to agree to 'what next'.
And incidentally, Eisenhower might have meant taking the Straits of Messina from both Sicilly and Calabria, as opposed to landing on the beaches of Sicilly and Calabria.
Recommend reading - Masters and Commanders by Andrew Roberts
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