No. The Army actually recruits more people every year then the entire Marine Corps.
The thing is, ever since WWII, the media loves the Marine Corps and the Marine Corps is much better at talking to the media and telling thier story then the US Army is. This is a problem the Army is trying to address this, but the media is the media.
The Army is almost 600,000. The Marine Corps is only about 180,000.
In simple terms, the Marines are a door opener. They invade the island or whatever, then the Army comes in and finishes the fight while the Marines get ready to attack the next place. Like an Airborne Division sort of, an Airborne division jumps in, then the ground forces met up with it, then the Airborne division is pulled out to get ready for thier next jump.
The Marines earned thier reputation in WWII. The Army did just as much and more, but the Marines had the forced entry part, and media was always there for it. The media didn't care about the clearing of the islands that could on for months, so they hardly ever covered it.
So even today, the Marines attact the media, just like they attract Hollywood as well if you look at the movies, its mostly Marines in movies. Most times the media and the Hollywood don't even know the difference between a type of unit. I have seen them call Soldiers "Marines" and they get equipment wrong all the time.
+++++++++++++
To correct some above answers:
The Army had a lot more infantry then the Marines do. The Army has 42 Brigades of combat Arms. The Marines only have about 9-12.
The Marines are not like Special Forces, they are more like an Airborne Division or Mountain Division, they are 3 divisions that have a specific mission of amphibous assault.