Yamamoto himself was pushing hard for an invasion of Oahu ("The Eastern Operation"):
It has commonly be supposed that any successful Japanese operation in the Central Pacific would automatically have culminated in an invasion of Hawaii. Certainly this is what Yamamoto had in mind. However, like the notion of operations in the Central Pacific itself, an invasion of Hawaii was by no means accepted within the Navy as a whole, much less by the Army. Admiral Yamamoto and his staff had been contemplating such a venture since the summer of 1941, but few others had contemplated such a notion. During the planning for the attack on Pearl Harbor, the idea had briefly been floated that a simultaneous invasion also occur against Oahu. However, such an attack was judged by Naval GHQ as being far too risky. In September 1941 the notion was dropped, though it was not forgotten by Combined Fleet. Thus, during the strategic debate that reemerged in early 1942, Yamamoto and his staff found themselves rolling not one, but two rocks uphill.
It didn't take long for both Naval GHQ and the Army to get wind of Combined Fleet's ambitions in the Central Pacific, whereupon Naval GHQ moved aggressively to put a stop to them. On 16 December, HQ sent Captain Tomioka down to Hashirajima to meet with Ugaki and discuss follow-on operations. While there, Capt. Kuroshima Kameto, Combined Fleet's "God of Operations," briefed Tomioka on operations aimed at seizing Palmyra, a tiny atoll that lay halfway between Hawaii and Samoa. Tomioka initially believed that this move was designed to help support follow-on operations into Fiji and Samoa, which was Tomioka's own favored axis of attack. Upon returning to Tokyo, Tomioka relayed the results of his meeting to both his boss, Fukudome, and to Fukudome's counterpart on the Army General Staff, Lt. Gen. Tanaka Shinichi. Tanaka saw immediately that Tomioka had been misled and that invading Palmyra was intended as a move into the Central Pacific and a stepping stone toward Hawaii, not Fiji or Samoa. He told Tomioka bluntly that the Army viewed any enlargement of the defensive perimeter as dangerous and unnecessary....
...In reaction to General Tanaka's misgivings, [Capt Tomioka] shortly had Capt Miwa Yoshitake of Combined Fleet staff come up to Tokyo to report further on Combined Fleet's plans. Miwa dutifully arrived on 27 December, 1941, and delivered a briefing on what was coming to be known within Combined Fleet as "Eastern Operation"--the invasion of Hawaii. Tomioka, alarmed, saw that he had indeed been given the wrong impression about Combined Fleet's schemes. He thereupon tasked one of his subordinates, Capt. Kami Shigenori, to prepare a logistical study of the proposed operation. Kami dutifully complied, and by 11 January Tomioka had all the ammunition he needed to shoot Combined Fleet's proposal down. While capturing Hawaii might be feasible, the logisitcal problems associated with keeping the islands' large civilian population supplied were substantial. Hawaii was not even remotely self-sufficient in basic foodstuffs. These necessities, in addition to the needs of the large garrison Japan would have to post there, would require at least sixy transport loads per month--a figure beyond Japan's meager resources. It was obvious that in the face of likely resistance from American submarines, these basic figures would need to be even further expanded.
While Kami was preparting his report, Tomioka was simultaneously working his superiors. At an Army/Navy conference in Tokyo on January 10, 1942, Admiral Nagano discussed the notion of Hawaiian operations with General Sugiyama Gen, head of the Army General Staff. Sugiyama and Nagano agreed that a direct attack on Hawaii was impossible, and that operations into the Fiji, Samoa area made better sense. General Sugiyama liked this option, because it would require less of a commitment from his branch of the service. Nagano liked it, because it was at least an indirect move against Australia.
Into this lion's den of stacked-deck politics walked Commander Sasaki Akira, a relatively junior member of Combined Fleet staff, to deliver yet another briefing to Naval GHQ on January 13th. His comrade, Miwa, not having gotten a strong negative reaction to "Eastern Operation" on his previous trip to Tokyo, Sasaki was undoubtedly expecting smooth sailing as well. Instead he was treated to Captain Kami's damning logistics study, followed by the Army's flat refusal to sanction an invasion of Hawaii, and topped off with the announcement of Nagano and Sugiyama's joint accord to proceed inot the Fiji/Samoa region instead. Sasaki thereupon retreated to Hashirajima to relay the news to Combined Fleet staff....
So...both the General Staff and Naval GHQ shut down Yamamoto's driving wish to invade Hawaii. Then, Doolittle bombed Japan:
The day after Doolittle's raid, General Tanaka privately told Captain Tomioka that he was rethinking his reservations regarding Operation MI. On the 20th (April 1942), Tanaka not only formally approved of Operation MI (the Midway operation), but also committed the Army to supplying troops for the assault. Even more intriguing, he informally asked Tomioka for more details on "Eastern Operation", which marked something of a watershed in the Army's appreciation for the scheme. The Army initially assented to Operation MI on the explicit understanding that it not be dragged into operations aimed at Hawaii. However, within a month, the Army had done an about-face on this matter, too. On 25 May, just days before the Nagumo force was slated to sail for Midway, the Army issued orders to several units to begin preparing for an amphibious attack against Hawaii. Training for the assault was to be completed by the end of September. Thus, against great odds, Yamamoto had achieved his goal--operations in the Central Pacific aimed at the destruction of the American fleet and the subsequent capture of Hawaii.
So, despite logistical limitations fully acknowledged by the Japanese, the invasion of Hawaii was a go. Obviously, the loss of their carriers at Midway forever ended this plan, but had Midway resulted in the destruction of the American carrier force with minimal losses in Japanese carriers, apparently the Army was planning to be prepared for an amphibious invasion by the end of September.
Had the Japanese not sent CarDiv 5 to Coral Sea to support the Port Moresby invasion, Shokaku and Zuikaku would have both been available to support MI, as had been planned. This would have given the Kido Butai 6 flight decks to the Americans' 3. Even after Shokaku was damaged, the authors point out that she still had enough aircraft intact and repairable that, had they been cross-decked to Zuikaku, the latter would have had a nearly-full complement of aircraft, essentially giving the Japanese 5 carrier groups with which to attack Midway. The addition of these assets may have resulted in a far different result at Midway.
Given a Japanese victory at Midway, Oahu would have been invaded in the late summer/early fall of 1942.