Three different ways you can take this, but I wonder about the outcome of each long term.
1. The Japanese take Midway, but at a high cost to themselves with most of their ships and planes being destroyed and a relatively low cost to the Allies
2. The Japanese force pushes the Allied navies out, with slightly more losses for the Allies than the Japanese.
3. A total Japanese Victory, with minimal casualties for them and almost the entire Allied force involved in the fight being destroyed.
Does any of these change the strategic situation at all? Is #3 even possible? What changes does this make to the Allied war effort?
Midway scenarios have been dug into at some length here at AHC.
The first scenario is probably easiest to address: Parshall and Tully in
Shattered Sword (see appendix 5 - you can read most of it on Amazon preview) are almost certainly right that any attempted Japanese landing on Midway Atoll would have resulted in "outright disaster." The Japanese landing force was actually outgunned and outmanned by the defenders, who had benefit of extensive coral reefs surrounding the atoll, with extensive beach fortifications, defensive guns up to 5 inch, and a platoon of M3 Stuart tanks hidden in the underbrush. Worse, the Japanese had little experience attacking defended beaches and little proper amphibious doctrine. As Calbear has put it, think of Tarawa in reverse, only with a quick and bloody repulse. To get Japan Midway, you pretty much certainly need Nimitz (or whoever is CINCPAC) decide
not to reinforce Midway at
any point in 1942; and that almost certainly entails some even greater point of departure.
And even if they do get it, they won't be able to keep it long. Even without U.S. interdiction efforts, the logistics of supplying and reinforcing it would be tough.
The other scenarios can be more readily had with reasonable, modest points of departure. The Americans were very good but they had some lucky breaks, as Nimitz himself said ("brilliance shot through with luck").
The thing is, though, it doesn't really change the long term trajectory of the war. Let's say the
Kido Butai survives in large part. What happens then?
Well, we know that Yamamoto's next plan after neutralizing the cream of CINCPAC's carriers was
Operation FS, a projected offensive in July (with no operational pause!) to secure the New Hebrides, New Caledonia, Fiji and even Samoa, in order to isolate Australia from easy American reinforcement. But it is now apparent that the IJN had almost no chance of getting any farther than Efate/Espiritu Santu, with a strong probability walking into disaster, as they had
no idea of how heavily the U.S. had reinforced these islands (they would have faced upwards of 22-35,000 Allied troops on New Cal alone, using nothing more than a brigade to try to take it!) and would have been operating at the fragile end of long supply lines under hostile land-based air cover even if Nimitz doesn't send
Saratoga and
Wasp to harass his flank.
See my discussion here from a few years back. One suspects, in fact, that Nimitz would have felt much as Sherman did when he learned that Hood was marching north into Tennessee after the fall of Atlanta: "D -- n him! if he will go to the Ohio River I'll give him rations!"
But set all that aside. Whatever Yamamoto manages to accomplish at Midway or Efate doesn't matter, because nothing short of an asteroid was going to stop the tidal wave of American war production that was going to arrive in the Pacific by 1943, and the Americans absolutely had the will to see it through. Nimitz can start with
Saratoga and
Wasp (and even
Ranger, if need be) and a goodly force of heavy cruisers, and by autumn of 1943 he'll be able to add at least five
Essex class carriers and six
Independence class light carriers, all operating their F6Fs and Avengers with vastly superior radar, dozens of escort carriers, as many as eight new fast battleships, and a massive array of escorts and amphibious landing craft and a vast logistical tail without precedent in naval history - all of which is already an overmatch for an
intact Kido Butai let alone one that's been roughed up at Midway, the New Hebrides, et al. In 1944, the tidal wave becomes a tsunami, with the USN fast carrier task forces of legend fully coming into their own.
In fact, Japanese victory at Midway might well not even lengthen the war. The immediate butterfly of any sort of IJN Midway victory would be the cancellation of WATCHTOWER and pretty much most or all of the Solomons campaign. In our timeline, the Solomons had no real strategic end beyond the attrition of Japanese naval air and surface assets, because Melanesia doesn't lead anywhere useful. Instead, Nimitz starts his offensive rolling in the Marshalls and Gilberts in 1943, and the attrition of the IJN happens here instead of in Melanesia, and most of those Japanese garrisons in the Solomons simply get added to the list of cut-off island-hopped outposts eating their belts and coconuts.
One other probably butterfly might be a modest adjustment in U.S. production priorities. Roosevelt will see an even more urgent need for more carrier decks, if the USN has lost 2 or more at Midway. There is little that can be done to accelerate
Essex class production (which was already running flat out), but you might see a few more
Cleveland class hulls made into
Independence-class CVL's, and a modest increase in escort carrier priority in the slipways.