What would be the effects of D-Day and the subsequent Normandy Campaign being bloodier for the allies? Not a complete repulsion, just harder fought with much heavier casualties and slower progress. Would the Soviet Union possibly conquer all of Germany, if Western Allies suffered significant enough setbacks? Would the Italy and Pacific campaigns be affected? Is Eisenhower's political career affected such that he never becomes President?
First of all how are the Germans inflicting heavier losses on the Allies? Second how much bloodier and slower? ITTL when would they reach Germany?
The Soviets would probably face more resistance than they did IOTL if there was a substantial delay in the Wallied advance, as they'd be more contained than IOTL, so Hitler would have no reason to use all the extra forces intended for the East in the West ITTL. The Battle of the Bulge forces would probably be used in the East and to greater effect too if well aimed. The Soviets didn't have the logistics to conquer all of Germany and they did stick to the OTL agreements about the division of Germany; they might conquer more of Austria and Czechoslovakia ITTL and maybe move west a bit more, but that depends on how the Hitler reacts towards the end; if he focuses more on the Soviets in the last 12 months they may not get any further ITTL.
But as I said it comes down to the specifics of the scenario, once we know those then we can give you a more detailed response.
Edit:
One potential POD is the Germans have gotten the Panzerfaust sooner than IOTL, so have something like the PzF 150 in large numbers by June 1944 (better armor penetration, reloadable for 10 shots, better range and accuracy). Of course that also likely changes the Eastern Front quite a bit too, but it would really complicate Allied efforts in Normandy without a major POD that really changes the course of the war to that point or adds anything major in terms of equipment or manpower to the German side. It would replace the Panzerschreck too, which is a big savings in terms of cost due to having one system instead of two, plus it would be less heavy, less complex, and most importantly less visible due to backblast.
Before anyone says that 'hey it's just a small arm, that doesn't matter in the overall scheme of things', remember that in Normandy the most common Panzerfaust was the Pzf 30 with 30m of range. That wasn't even the most produced Panzerfaust of the war either, which was the Pzf 60 introduced in September 1944 (well after Normandy), yet in Normandy Panzerfausts they were one of the most deadly anti-tank weapons despite being only available in quite limited numbers and only having 30m of range (which was optimistic for those models). In 1944-45 they accounted for nearly as many Allied tanks as German tanks. Having 1945 levels of Panzerfaust availability with 5x more range and better penetration the OTL Normandy model and more importantly very good anti-infantry performance would be a very serious firepower enhancement. See how well the RPG platform has performed historically in Vietnam and Iraq and Afghanistan.
Here his how they turned the Panzerfaust into a very potent direct fire anti-infantry weapon:
Two of World War II's most distinctive weapons, the Panzerfaust and Panzerschreck offered German and other infantrymen the ability to destroy enemy tanks singlehandedly at close ranges. While the Panzerschreck owed its origins largely to the US bazooka, the Panzerfaust was a revolutionary design...
books.google.com
Basically to the PzF 150 they added a fragmentation sleeve and an auto-destruct feature that would activate in 3 seconds which meant they could achieve airbursts like the modern RPG-7, so it could function as a mortar replacement. Effectively then it would be a handheld artillery piece. Modern studies effectively range an 81mm mortar as being worth 3x machine guns and an RPG as nearly as effective as an 81mm mortar in combat, so passing a PzF 150 out to every squad with 10x rounds would mean every squad has in effect their own direct fire 81mm mortar. Rather than being 'small arm' it would effectively be infantry artillery with good anti-tank abilities. I'd imagine that would cause the Wallies quite a lot more trouble in the terrain of Normandy than IOTL when the Panzerfaust was still a new weapon with limited abilities and in limited quantities.