I think you need a series of POD's. You need a more ambiguous war, probably going back to late 1930's. You don't need all of these, but enough to add up. And yes as others said, Japan must not attack.
1) Breaking Munich hurt Hitlers reputation. If we can have it so there is more of a reason for Hitler to come in, it helps a lot. Not full justification, but Czech are also bad. Think something like IRA (Czech Republic Army) blowing up enough stuff to make it murky. Maybe one bomb goes off near US Embassy or something. Now this may be too far back for you to be close enough for OTLish WW2. So to next one.
2) Like #1 with Poland. Massacre by Polish militia in Danzig or whatever. Or Soviets hit Poland same day as Germans. Again, maybe POD too far back for your liking.
3) Get UK in Finland. Even a regiment would be enough to confuse the USA public on who is good and bad once Germans and Soviets start fighting. Massive, Massive butterflies.
4) Norway. UK sailed before Germans or very close to this. Have it get into USA papers that UK attacked first. Something like some of the leaks in USA press in war but for UK. A few days before the British leave, a USA paper gets the scoop. So 24 hours before Germans land, NY Times runs article saying "British invade Norway". Does not matter too much if the information is false, that is the paper got information from source that did not have the information. I think by now you will need to have used some POD, so we get a situation where it is murkier before France falls and scares people. At first blush, this is where I would start my POD for a TL "Hitler has better PR; Story of American Home Front". Not a winner for Germany, but who says every TL has to have a different winner in a war.
5) Better SS reputation. (note better does not mean good). There are posters on the board who believe Hitler was incapable of any slight moderation here. I am not one of them. I think with the right people and arguments, he might be to see the benefits of being less obvious in what he was doing. 400K of 500K Jews were allowed to leave Germany prewar, without possession of course. Unfortunately most did not run far enough away. Simple things like not making official PR films that gloat over the killings help. Banning cameras at the mass graves. We could also look at more radical options waiting until after the attack on the Soviets to treat Poles so badly, so publicly. The Nazi's were proud of what they were doing.
6) Something to make/remind USA of fear of communism. Not enough up on subject, but I am sure some way to make USA public more aware of Stalin. Some Soviet assassination on USA soil of Russian exile. Soviet movie villifying USA is translated and show at some theaters.
7) FDR was trying to get justification for war by actions in Atlantic. You need something here to backfire on FDR. We talk at times on the USS Texas coming close to being attacked by Nazi. We need some mistake by US Navy to cause issue. Say sinking some Spanish naval ship. Shooting at Swedish merchantman mistaken for commerce raider. Paper makes issue of FDR breaking law, at least effectively making the case. The stuff being smuggled across border to Canada as "scrap" is scandal. Add bribes, drugs, hookers or something to story it might gain traction.
These types of POD should give you a shot at some murky feelings, maybe protests.