It has to be remembered that as the Red Army continues to maul the Wehrmacht, France becomes easier to invade with each passing month. And contrary to popular opinion, Stalin was not interested in screwing over the West and conquering the whole continent. I'd say that as a worst-case scenario, the Western Allies get France, the Low Countries, Norway, and at least half of Italy.
I'd say worst case, the WAllies get all of Italy (well, save for those bits which went to Yugoslavia, of course. Even leaving aside that the WAllies are already moving north as others have pointed out, the Soviets are fundamentally uninterested in climbing over the Alps.
The big question is how succesful bagration will be with a failed D-day landing.
Well, the Germans will mount a harder counter-blow towards it's end that'll shave off a 100 kilometers in it's gains and give the Red Army some additional losses, but it won't fundamentally alter the prior operations. Likewise, all the German reinforcements that get transferred in from the west are gonna be sucked into patching up the hole left by AGC, so there's no reason to expect the Balkan campaign to go too much different until the Soviets hit Hungary. It'll be the winter fighting in Hungary and Poland that'll see the big differences in Germany not having a western front, but even that's still just a case of slowing the Soviets down by a few months and costing them several hundreds of thousands more men which, given that the Soviets ended the European War with almost one-and-a-half million men still in replacement training, isn't going to fundamentally alter the course of the war. The Germans just don't have the combat power to hold off the Soviets by the summer of '44... they hadn't had it since Stalingrad, really.
Given how close BAGRATION was launched there probably not a lot the Germans can reposition to prevent success. Perhaps a late summer or early autumn counter attack might be productive. There is also the question of if Op BAGRATION would be launched were OVERLORD to fail early on. Did the Red Army have a contingency plan for that?
Conception and planning for Bagration was done in April and May, before D-Day went off, and it's execution was conceived of being totally independent of Overlord's success. The biggest impact on Soviet planning and execution I could see it having is making the Soviets more wary of German reserves showing up in the east towards the end stages of Bagration and decide to reign it in sooner.