You remember incorrectly. If my memory serves me, the original option pushed by Churchill was an invasion of France, but this was vetoed by FDR as he wanted a quick and decisive US victory for political reasons. Operation: Sledgehammer, as Churchill's plan was caused, was a temporary beachhead in Western France which would not have liberated the country, but would have served the purpose of letting up pressure on Stalin - who was still on the back-foot at this time. FDR liked it at first, but then realised that there'd be a lot of US casualties and that a temporary beachhead for the sole purpose of helping the Russians could be seen as a defeat by the American people, so he vetoed it. Churchill then offered up Torch, which wa a good idea with poor execution. FDR is largely responsible for that poor execution. You're right about what FDR wanted though. He was more concerned with domestic political considerations than the war. Another reason I never much liked him.
Ehh Actually Operation Sledgehammer, Operation Roundup and Operation Bolero all originated from the American Military Generals i.e Marshall and his subordinates. Operation Sledgehammer was a cross channel invasion of limited scope to be launched in the face of collapsing Russian positions, the limited objectives were to basically reduce pressure on the Russians. Roundup was slightly more serious, aka an actual invasion, unfortunately/fortunately the Allies didn't have the capacity to carry these operations out (as the Dieppe raid proved, such operations are quite hard). Operation Bolero was the build up of American forces in the UK for an eventual invasion of France.
Now Brooke the British CIGS hated Sledgehammer and Roundup, and strongly opposed them, pointing out lack of shipping, the waste of resources and other factors. However the Shipping is the strongest point. Churchill loved Bolero, as it put American forces on the ground in case of invasion, something he wanted. However Churchill was convinced by Brooke that Sledgehammer/Roundup were not to be pursued, at least not so soon until proper resources had been built up.
Churchill quite cynically I suppose, proposed Operation Torch, this helped him in Africa and also ruled out an Invasion of Europe proper in 1943. Brooke and Marshall both disliked it. However Churchill convinced FDR, and thus the generals were ordered to make it so. Now in my mind Operation Torch, as the first operation in Europe was always going to have teething problems, they also weren't sure how to treat the french, which was just plain difficult. So on the scope of things, it wasn't the perfect operation, but it did the job.
FDR did mess up with Darlan, bit strange that both the UK and the USA had 'pet' frenchmen for a while, not sure what FDR hoped to achieve.
They'd have used far less troops if they hadn't buggered Torch up. Or rather, they'd have used more ships and troops, but they'd have won quicker and more would have become available. Then there was always the possibility - pretty likely - that many Vichy troops would defect to De Gaulle or Giraud if they'd been included in Torch at a higher capacity. Certainly the FDR-backed Darlan appeasement alienated the Free French. If they'd handled Torch with any degree of skill the invasion of France could have been launched in 1943.
I know they tried to include Giraud, he was a bit demanding however (wanted to be commander of the entire operation?), can't remember de Gaulle, but I don't think Churchill liked him much, and didn't want him out from under his thumb anyway.
With regards to buggering Torch up, perfection is difficult, and the way FDR had set up Politics at Washington didn't really help. I don't expect perfection however, I don't even expect very good at this stage, maybe just decent.
It was also pretty well defended. I've got no real problem with an invasion of Northern France, I just think there were better options available at the time. By this point, North Africa and Egypt were perfectly safe supply depots themselves.
North Africa, Egypt etc didn't have the infrastructure to build up resources to the degree that Britain had the capacity to serve, all such operations would have been much more limited. More to the point the implementation of bolero had meant that they had been building up troops in the UK, since before Operation Torch was launched, it would have taken a long time to move such a large amount of troops to another staging area, since they would have had to wait till these staging areas were subsequently captured.
Furthermore the Americans (and this emanated quite a lot from the American Generals as well) thought that the British were being well, cowardly about going into Northern France and by this point the Americans had most of the material and resources and bullied the British into this position too. The Americans weren't as worried about casualties. It did make a certain amount of sense, go for the heart of the problem, Germany, from the strongest power base you have in the region, Britain. But the blame for such an operation doesn't rest completely on FDR's shoulders, his military advisers were pushing it hard.
And the Americans were stupid to do it. It was patently obvious the Soviets were a threat. One need only look at their activities before Operation: Barbarossa to have proof of that. Admittedly, the secret protocols of the Molotov-Ribbentrop Pact weren't yet known, but it was still clear that they'd seized the Baltics and invaded Finland with no justification whatsoever. On top of that, they were communists, which by itself was reason for concern among capitalist nations. Promoting British interests may not have been America's goal, but FDR shamelessly caved to Russian imperialism in Eastern Europe while fighting British imperialism in the Mediterranean, Africa and Asia. That was just stupid. Truman tried to fix that, but Britain was already too weak to hold its empire after the war.
I can agree with this, Early on there was some hope that the Americans could go back to to letting the British take care of things. This proved false over the course of the war, and Americas growing up period was rapid and full of mistakes, Unfortunately the Americans were still fairly short-sighted and couldn't really fully accept the consequences of the war . (Come on, they were used to having this tiny army and just sort of sitting out and pointing at the Old world!). Now if you put any American president from recently back in FDR's shoes I'm pretty sure the outcome would have been different, but now the Americans are used to being on top and thinking ahead...well sort of.