Must admit I'm highly dubious about the video, including the war going on until 1947. The latter is basically a throw away line at the end of the discussion by the commentator with the historian given a kind-off yes it might go on into 46 or 47. I must admit I listened to the 1st couple of sections then jumped to the last bit where they were talking about a failed D-Day but would say:
a) An early comment about Omaha beach being the most heavily defended is inaccurate. According to some reports it had relatively few defending troops on it in the 1st hours. What it did have was the natural defences of the cliffs which made getting off the beach slow and bloody and the sinking of the Sherman tanks allocated for the beach because the man commanding the ship they were on ordered their launching at too great a distance and they got swamped by the waves.
b) There was the suggestion that it would take at least a year before another attempt in NW Europe was launched but I'm doubtful of this. Assuming a quick defeat, which is the only really likely option relatively few men would be landed and lost and their equipment would be minimal. The big issues might be the loss of para units, amphibious vehicles and possibly the Mulberry harbours if their deployed. If their not significant factors then if the commanders are willing - talking about up to political level of course you could conceivably try again in July. Which might have better impact both because of lessons learnt, the Germans not expecting it and also them probably having had forces drawn east by the destruction of Army Group Centre. What would be an issue is if you can't get it launched in July or August worsening storms could mean it has to be ruled out until the following summer. However in that case you can move forces elsewhere and of course the strategic bombers stop hitting transport links in France and go back to what their commanders want them to do in hitting German cities.
The historian made a comment that while technically kind of accurate is misleading in relation to the reason for such a delay. Namely that forces for this invasion had been building up since early 1942. To a degree but the big issues in 42 and parts of 43 were that Britain couldn't afford to support masses of US forces because of the U-boats threatening the Atlantic supply lines, the US had no real forces/equipment to send and both powers were reeling from the initial Japanese attacks in the east. By mid 44 those issues are removed and the large US forces that continued to flow into N France from the US would still be coming and with a little effort could be moved towards the Med.
c) If it was decided that another attack in the north wouldn't occur until 45 then the bulk of those forces/reinforcements could be switched to join those already in the Med with a range of operations available. Operation Dragoon was briefly mentioned and it could still go ahead, with additional reinforcements from some of those forces now sitting in the UK or crossing the Atlantic. Due to the terrain/logistics there are less chances of a break-out being fast here but those same factors mean the Germans have problems reinforcing the region. This could be accompanied or replaced with further landings in Italy to bypass the Gothic Line since amphibious units would be available for landings on both coastlines in number as well as land attacks on the defenses. Also there would be options in the Balkans where progress is initially likely to be slow due to the terrain and poor logistics but once things get moving the broad front available could mean allied forces say meeting the Soviets on the lower Danube.
d) I can't see Churchill losing power over the issues. There have already been disasters enough under his leadership and if the key factor is a failure on Omaha beach many Brits are likely to see that as the Americans being the reason not their own leader. Roosevelt might not stand in Nov 44 but that could be because the stress of the failure could cause a faster collapse of his health which makes it impractical but whoever the Democrats choose as leader is almost certain to win. The party has seen the country out of a devastating depression and led them them to a number of victories in the war. There have been errors and mistakes but their been largely hidden by wider successes or propaganda.
e) The bomb is only mention twice with a question of would it be used against a still fighting Germany - which unless Germany was in the last stages of total collapse I would say definitely yes. Then a question of would we threaten to use it against the Soviets to try and stop them coming too far west? Which seems a stupid comment as the implied alternative is that the western powers are saying leave western Germany occupied by Nazis until we can reach them.
f) I can't see the Soviets ending up on the French border along its length because that would suggest that the Germans are putting defending France and the low countries from western forces ahead of defending the Ruhr let alone Berlin. You could see them occupying more of Germany, possibly even up until the Rhine but that's unlikely even if the allies take their time a lot. Occupying Denmark would however be an issue in such a scenario but France, the low countries and at least the Rhineland west of the river would be under allied control. This would give the Soviet empire more resources but also mean they have the task of rebuilding a lot more of Germany - which they would worsen by initially looting it heavily as they did their zone OTL.
g) I can't see the US deciding to give the Pacific top priority because they would still see Germany as the primary threat. It has a level of technological sophistication that Imperial Japan can't match and still has much of Europe - including a lot of industry under its control. This would be demonstrated by the V-1 and later V-2 attacks and most of all possibly by fear of the Germans getting nukes 1st, which wouldn't be a concern with the Japanese. - We know now how much of a mess the German a-bomb projects were but that wasn't clear at the time and the allied leaders wouldn't be willing to risk it.
I would say the probability if D Day failed and another landing in N France was impossible/decided against in 44 then the war would end in 45, albeit somewhat later and depending on the timing nukes might be used against Germany. Russia would probably have more of Germany and probably Denmark but the unless they really screw things up the allies would have the territories mentioned in f) above, probably all of Austria and quite possibly say Serbia/Montenegro and Bulgaria. Stalin would be angry at the failure in Normandy in 44 and accuse the allies of deliberately failing so the Soviets would take even heavier losses and the could have icy relations from the start and no real agreement of the handling of Germany and other occupied areas. As such the cold war starts pretty much immediately and no Soviet invasion of Manchuria. This has a bad side in that the war in the Pacific will last longer with more losses for the US and the occupied territories and especially for the Japanese who are likely to see more fire bomb attacks, nukes and starvation. On the plus side it probably also means the KMT stay in control in China and Korea is united under a pro-western leader.
As such a bloodier WWII that lasts somewhat longer with the primary sufferers being the Germans, Japanese and Soviets. Total US and British losses might actually be somewhat less with a shorter fight against N France against weaker opposition, especially if an invasion of Japan is avoided.
Anyway thanks for the video and sorry this has been so long a reply but trying to cover all the bases.