In short no that is wildly inaccurate.

While the American Pacific fleet was smaller than the Imperial Japanese Navy (IJN) in 1941, all their aircraft carriers (their most strategically important ships) had been away from Pearl Harbor during the attack, and were unscathed along with the majority of American destroyers, cruisers, and submarines. The Amphibious invasions in WWII relied on first establishing naval and aerial superiority before attempting a landing and even then it wasn't a sure thing (See the Dieppe raid). In addition to war ships an invasion fleet needs troop transports which are slow, bulky, and lightly armed and armored. Their is no way the IJN would dare send a fleet in force anywhere near the American mainland before absolute naval supremacy had been established, which it wasn't after Pearl Harbor.

But even if the Navy decided to give the Japanese a freebie and sail on up to Santa Monica Pier to disembark they would still have to fight a ground war against a country with a population of 147,500,800 people, compared to Japan's 71,900,000. Not to forget that a good portion of the Japanese army was engaged in fighting in China, and South-East Asia. And though the American army was small in 1941, it was standard U.S. policy to rapidly mobilize in times of war, calling up reserves and recruiting and training new troops, which is exactly what they did after Pearl Harbor. They would also half to contend with American Geography and supply lines, this hypothetical army would be lucky if they could make it to the Rockies before running into some heavily defended choke points.

TL;DR The IJN was in no position engage in such a risky operation as a invasion of the American mainland, and even if they were the army would quickly be bogged down fighting an increasing large defending force of a country bigger than their's by every conceivable metric. And the fictional general would go down in history as the biggest pessimist since Chicken Little.

The 'what-if' popular 'historians' like to bring up bogus claims like that, usually for two reasons.

First, since the rise of the internet and information age, we live in a society oversaturated with information. The more bogus and absurd a claim, the more 'clicks' and 'attention' it will get. Second, in WW2, Allies had a tendency to overestimate enemy's abilities and forces ( when it came to propaganda ), sometimes even inventing their own fifth-column myths. Hayward's Myths and Legends of the Second World War has a nice collection of these; allied propaganda doctrine generally believed that propaganda should be utilized to keep the home front vigilant (also, makes war bonds sell better), by blowing the threat of the enemy out of proportions. ( "We will fight them on the beaches..." even though Churchill was aware any kind of a Sealion was impossible to pull )

In any case, those kind of myths persisted through pop culture, and as such become quoted, and again blown out of proportion, where historical accuracy is sacrificed for the sake of spectacle.

Parshall and Tully's Shattered Sword has a specific chapter dealing with 'what-if' scenarios, one important here a potential invasion of the Hawaii islands. The popular observer thinks of world war 2 and thinks of unstoppable machines of war, tanks, ships and airplanes waging war, without understanding this mechanized conflict has a crucial aspect - supply.

With most of the IJA tied down in China since 1937., IJN simply didn't have either the supplies ( keep in mind once you occupy an area, you have not only your own soldiers to feed and supply, but local civilian population as well ), either the supply train (cargo ships) powerful and numerous, enough to support such a long-range operation as invasion of Hawaii, not to mention West Coast, not to mention Chicago.

For other IJN logistical failures of supplying troops in relatively hostile territory, take Guadalcanal in 1943., where dozen thousands of Japanese troops died due to supply related problems, whether from starvation, malaria, or related complications.

For further reading, check Parillo's The Japanese Merchant Marine in World War 2 to fully understand the capacity (or rather, undercapacity) of the Japanese naval supply train in WW2.

If you are still looking for answers, here's my two cents.

What I found lacking in the two previous responses to your question was context. In the context of the scene, the general is arguing against the use of aircraft carriers (equipped with typical air wings - aka not the B-25s they end up using) to strike at the Japanese home islands, since the loss of those carriers would leave the fleet, and by extension, the country, vulnerable.

Is the argument completely ridiculous? Absolutely not. Is it an exaggeration? Yes. Should you read too much into the general's argument? No.

One would hope that the powers that be would consider the worst case scenario that could result from important decisions, and that is the case that the general was trying to invoke - a worst-case. Supposing that the United States lost half of its aircraft carriers in January of 1942, what is a plausible worst case scenario? Could the Japanese engage the US Pacific fleet in a decisive battle, crippling it and putting it out of action for a couple years? Perhaps. Could the Japanese invade and successfully capture Hawaii, the closest major pacific supply hub to the United States? Supposing that the Japanese could manage to organize the logistical resources to invade the United States - something we now know to be preposterous but something that simply wasn't known at the time (experience gained at Dieppe and other amphibious landings informed the Allies greatly) - then what would be the worst case? What if the Japanese war in China ended? The United States Army only had a handful of active formations at hand - perhaps 5 or 6 divisions worth, in addition to perhaps 25 divisions worth of national guard units (that would have to be equipped and would take some time to mobilize). Even if the Japanese only landed with 20 or 30 divisions, they would have easily overwhelmed US Forces hurriedly deployed in the West. (Note that the severe supply problems the Japanese experienced later in the war don't really apply to this worst-case scenario, given that they were the result of a highly successful US submarine anti-shipping campaign.)

The point of the general's argument was this: The United States was simply not ready for war. Every effort must be undertaken to defend the US homeland while the United States builds its strength. Given that the oceans and the navy are the country's primary shield, any weakening of that defense could be disastrous and at that point in the war, risking America's fleet carriers was akin to risking defeat.

You have to remember that the American story from World War II was one of preparing, one of building up. Building up military industry, building up army formations, building up army doctrines, building up naval strength, etc, etc. Even by D-Day, mid-1944, the United States had relatively few combat-ready divisions compared to Germany, despite Hitler's Germany having barely a bit more than half the population of the United States.

Long story short, in the context of the scene, the statement was appropriate. That being said, it would probably not be appropriate to extrapolate too much from the scene, given that it is a worst case scenario, and people rarely talk about such extreme/unlikely cases (except when it comes to North Korea, because reasons -> sarcasm).

An interesting sidenote is that when Hitler was asked (by Time Magazine I believe) if he had any designs on the United States, he compared a German invasion of the United States to an Invasion of the Moon, not that Hitler is the most trust-worthy person in history.