First things first: you've got a nomenclature error here and hopefully I'll post here before a Marine does. :)
The Marines aren't part of the Army, they're part of the Navy (though they don't like to admit it). As for the toughness part, the Marines are known for their esprit de corps and as such utilize it to the full in their advertising and their public promotion. However, if you truly examine most American veterans you'll find Airborne/Airmobile, Ranger, and other Army vets with just as much pride in their service branch. It can be argued, though, that the Marines have promoted it better than the other branches of the United States Armed Forces.
Marines earned a great deal of deserved credit for their island-hopping exploits in World War II but it should be noted that other armed forces had equal roles in the Pacific (the Army, for example, did most of the heavy lifting in the recapture of the Phillippines), and the United States Eighth Air Force in Europe suffered more combat casualties during the war than the entire USMC. That in no way detracts from the Corps' performance or importance.
Marines also added to their reputation in Korea, though again, their exploits were not made in a vacuum. But for their type of work, they have always attempted to recruit those who they know will fit their rigorous physical requirements. Ergo, "The Few, The Proud."
As a piggyback, if I may, the USMC seems unusual compared Marine Corps in other nations, in that it's pretty large and has a number of jobs - Marines guard US embassies, for instance. Most others, including our own Royal Marines, have evolved into smaller commando/special forces type units.
Even the Russian Naval Infantry, which is comparable in terms of size, doesn't have its own independent air arm, for instance.
Was this strength and "mission creep" a result of the increased prestige of the USMC after WW2 and Korea, or just a natural reaction to the changing needs of the Cold War?