Who would the Party pick in Roosevelt's place? Keep in mind Wallace would likely launch a third party bid for the WH as IOTL.
I think it all depends on the actions of Roosevelt's Third Term...
I doubt it would be as rosy a utopia as many New Deal enthusiasts would claim. I have my doubts that FDR would have even ventured down the path Wallace did nevermind do so successfully. Honestly, I think FDR's going to stay as far away from any version of Wallace's 2nd New Deal as possible.
I think it is fair to say however, that under Roosevelt the bipartisan nature of his cabinet would continue. Stimson, Knox, Hull, and Forrestal will all probably stay onboard and continue to aid in the prosecution of the war. Connected to this, without Wallace's shake up of the Navy James Doolittle's planned raid on Tokyo and Yokohama in April of 1942 probably goes ahead as planned. If they're successfull (let's assume they are) The Japanese will be forced to pull back large numbers of fighters for homeland defense and American morale will achieve a huge boost.
Of course, if the Enterprise and the Hornet head off to Tokyo, that means that the Yorktown and Lexington are stuck on their own facing off against the Japanese in and around Port Moresby. Without the arrival of the Enterprise and Hornet, the Shokaku and Zuikaku probably escape and live to see another day.
As for the remarks that FDR would focus solely on Europe had he lived, I have my doubts. I doubt that his cabinet, congress, or the nation would allow him to ignore the "threat" of Japan. Though FDR will certainly put a more public emphasis on the war in Europe, the powers that be will ensure that the Pacific Front is well taken care of.
With FDR in charge and without a second New Deal or the issues of civil rights, the 1942 mid-term elections are a cakewalk for the Democrats who see their New Deal Coalition persist into 1944.
Another thing to take into account is that with FDR in charge, Anglo-American relations will be exponentially better. Had he lived I have no doubt that Churchill would have been able to talk FDR out of a 1943 invasion of Northern France. Now I remember reading that around late 1942 the British were planning for a full on invasion of Vichy French Africa... Operation GYMNAST or something like that. Perhaps Churchill and Roosevelt use this as a chance to introduce Americans into the European Theater of Operations...
Combine an American supported GYMNAST, with an earlier defection of Admiral Darlan and you've got a major headache for the Germans. I'd say that with most of North Africa in their hands Rommel is pushed out of Africa by mid 1943 at the latest. Then having already committed so many forces to the Mediterranean FDR and the Americans would be more likely to support an invasion of the Balkans or perhaps (more likely IMO) Italy seeing as it has slightly better terrain.
Now I doubt any of this will affect the Eastern Front all that much. Hitler's not going to bother defending North Africa when he's got much bigger fish to fry in the Soviet Union. All he'll do is shore up defenses in Italy and the Balkans and get Rommel out of Africa ASAP to save face...
Another thing to take into account are the effects of more Anglo-American lend lease and Anglo American cooperation in regards to the Atomic Bomb. More lend lease probably leads to lower British casualties and more offensive power in the Pacific (Burma offensive?) and in Africa. Cooperation on the A-Bomb might lead to earlier development (only slightly)
Come 1944 you've got a WWII that's looking a lot better for the Western Allies. It's fair to say that Wallace bungled it big time, so without him the Allies are going to do better no matter what. How much better is anyone's guess. I think the above scenario is somewhat realistic if not a bit ambiguous.
Anyway fast forwarding to 1944 you have the Allies in firm control of Africa and probably half-way up the Italian Peninsula. Northern France probably gets invaded after the Allies bog down in Italy but this time the Allies are ready. Perhaps they'll have learned by then that landing directly around a major port isn't such a good idea. At any rate, distracted by events in Russia and in Italy the Allies should be able to carve out a relatively big slice of Northern France for themselves. Perhaps Patton can restrain himself from slapping that soldier and stay in charge long enough to impact the conflict somehow... Meanwhile in the Pacific the Americans are Island hopping away probably focusing on the Philippines given MacArthur's insistence on returning...
All in all things look good for the Democratic Party. However FDR's health is failing and he can't consceinciously run for a 4th term. He announces his intent to resign in late 1943 leaving the DNC to pick his successor. Though he'll initially favour Wallace I think the bulk of the DNC will force him to pick another candidate, honestly I think FDR will eventually side with Cordell Hull as his successor. With things going so well and with him being a relative nobody, Wallace might not run for the Progressives afterall giving Hull a free ride on FDR's coattails into the White House...