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If Iran decides to fire 300 drones in a swarm attack on the carrier strike force, and each destroyer fires at least two air defense missiles at those drones, that would require 600 air defense missiles. And there is the problem… If each destroyer is carrying a load of Tomahawks, then they are only carrying a maximum of 100 interceptors. Not only will the destroyers not have enough interceptors to fend-off the attacking Iranian drones, they will deplete their missile stock.

That ignores the most valuable asset of a carrier strike group, the air wing, 48 aircraft capable of shooting down drones and cruise missiles. Or the F-15s and F-16s available at bases in the Middle East, which can also shoot down drones and subsonic cruise missiles, equipped with APKWS laser guided rockets. One F-15 or F-16 can be equipped with up to 42 APKWS rockets. That's a deep magazine for shooting down drones and subsonic cruise missiles. Propeller driven one way attack drones fly slowly, given the potential position of the USS Abraham Lincoln aircraft carrier strike group around Oman, these drones will take 8+ hours to reach it. That's 8+ hours to figure out an intercept solution before they get close to the carrier and require the destroyers to engage them.

There are multiple models of one way attack drones with the required range, but how many are equipped to track and engage a moving target at sea? That's going to require some sort of datalink to give the drone an updated position of the moving target so it can alter it's course towards it. Most are for striking static land targets, which won't be able to target ships, and reduces the available inventory of appropriate drones.

As for subsonic cruise missiles, their significantly increased speed makes them more of a threat and a viable tactic for a swarm attack on a target, they'd probably take between 60-90 minutes to reach the position of aircraft carrier. But again, Iran's short range cruise missile arsenal won't have the required range, and their long range arsenal for hitting static land targets won't be able to engage ships, Iran will be limited to using longer range cruise missiles with the guidance systems needed for anti ship missiles (Paveh anti ship version). And the cruise missiles can be engaged and shot down by aircraft, including those equipped with APKWS.

Anti ship ballistic missiles (ASBM) are probably Iran's most viable weapon. They can't be shot down by aircraft, take 6-12 minutes to arrive, and require the use of specialised interceptor missiles (SM-3 and SM-6) to shoot down. However, the aircraft carrier will likely be positioned outside the range of most of Iran's shorter range ASBM arsenal, requiring the use of more exotic longer range weapons to engage the carrier strike group, like Qassem Basir. Not all of Iran's ballistic missiles are anti ship capable, the ones that are usually have electro optical guidance (a camera) in the warhead to try find and then steer the maneuverable warhead/re-entry vehicle towards the ship. This is quite different from a cruise missile and difficult to get accurate enough to hit a ship, yet alone a moving ship.

That's the main effect Iran's arsenal of shorter range anti ship weapons accomplishes, keeping the aircraft carrier further away at this stage.

As for surface strike, yes the destroyers will have a few Tomahawks and likely expend them very quickly. But that's not the only option for cruise missile strikes. An Ohio class guided missile submarine can be equipped with 154 Tomahawk cruise missiles and get very close to Iran, much closer than surface vessels. And then there's the AGM-158 JASSM series of cruise missiles that can be launched by tactical fighter aircraft in the Middle East, and strategic bombers flying out of the continental USA. One F-15 can carry up to 5 JASSM, one B-52 20 JASSM, one B-1B 24 JASSM. And the USA is not going to be firing cruise missiles endlessly. With the kind of aircraft they are moving towards the Middle East (F-35s and EA-18Gs with NGJ pods), the US plans to enter Iranian airspace, suppress air defences and conduct an air campaign in that manner, if the decision is made to do so.

I also don't think they'll send the destroyers to reload Tomahawks once they've fired all of them, a more relevant constraint is the amount of anti ballistic missile interceptors onboard the destroyers (SM-3 and SM-6) vs stocks of Iran's long range ASBM arsenal (Qassem Basir and Zulfiqar Basir), and any sort of left of launch defeat strikes the US will aim to impose on these long range ASBM fireteams. If destroyers run out of SM-3 and SM-6, they'll need to go and reload somewhere. As for intercepting cruise missiles and other aerodynamic targets, the Evolved SeaSparrow Missile (ESSM) can be quad packed into a MK 41 VLS cells using the MK 25 canister, meaning a single MK 41 VLS cell can hold 4 ESSMs. So that's worth keeping in mind, it's mentioned in the article.

In a "kill chain", the required steps to successfully complete and verify a "kill" in military doctrine are Find, Fix, Track, Target, Engage, and Assess (F2T2EA). That's a lot more difficult than it seems, especially with regards to naval warfare. This is why a lot of the constraints above apply.

So no, I don't think the aircraft carrier strike group will run out of steam within days, unless Iran manages to fire a large amount of long range ASBMs to exhaust interceptor stocks and force the carrier strike group to go defensive and leave the area.