King would argue that they've already tried things Nimitz way and lost - badly. Better to hold the line and wait for the Essex and Independence class to come out in force then confront the Japanese with sheer numbers.
Not so sure about that.
King was not a man to back away from a fight. He'd also worry greatly about the morale effect in the fleet of hiding in port, refusing to parry a Japanese offensive.
Instead, I can see him demanding that
Ranger be deployed to the Pacific, for starters, and maybe
Washington, too (hell it was going out there anyway in the fall). It would be hard to deny him.
Ranger has its weaknesses, but at this point, it's all hands on deck, and now you have a three deck fast carrier force once again, roughly, and plenty of big AA platforms to escort them (if you can fuel them).
Meanwhile I expect they would ferry as many aircraft as they could to the big three islands, and step up submarine patrols, since Melanesia is such an obvious next target. Be more interesting to ask what happens with regards to Port Moresby. I think it is unlikely Nimitz can help, but what MacArthur and the Aussies would do there...interesting to think about.
Once HYPO et al catch wind of a Japanese offensive, I think a lot would depend on how much they learn about FS. If it looks like the full Kido Butai, King might still push for allowing Nimitz to send the carriers down there - preferably not under Halsey! - but under tighter restrictions. Maybe you let Nagumo get bloodied during the attacks on Efate and Espiritu Santo, with the carriers only hitting them at the back end if they've been damaged enough to make the bet worthwhile. For example, maybe a squadron at Efate gets lucky and disables one or two of Nagumo's carriers.
I think Roosevelt would be reluctant to second guess such an argument by King, at any rate. He seems to have been willing to let King and Nimitz run big risks, like he did with the Doolittle Raid.
I also cannot rule out that King might even swallow his pride and ask for a Brit deck or two to beef up the force - since, well, that is what happened in 1943 OTL, after all, and the need here is even graver. Granted that even if Churchill acceded, they wouldn't be available in theater until sometime in the fall, presumably to counter the second phase of FS.
Still, I think we CAN say that all offensive operations are out of bounds until well into 1943, and there are some
Essexes and
Independences in hand. Maybe the odd raid, but otherwise...