First off, the standard issue M16 and M4 (A2 and A4) are capable only of semi-auto and 3 round burst. While there are M16 and M4s that are capable of full auto fire, they're generally not issued to the troops. And shotguns are in wide use, especially for close quarter combat.
From HQMC Fact Files
United States Marine Corps Weapons & Equipment
12 Gauge Shotgun
Primary function: Manually operated (pump), repeating shotgun.
Length: 41.75 inches (106.05 centimeters)
Weight: 8 pounds (3.63 kilograms)
Bore diameter: 12 gauge
Maximum effective range: 50 yards (45.7 meters) with "00" buckshot load
Unit Replacement Cost: $600
Features: The 12 gauge shotgun is a manually operated (pump), repeating shotgun, with a seven-round tubular magazine, a modified choke barrel, ghost ring sights, and is equipped with a bayonet attachment, sling swivels and a standard length military stock with phenolic plastic buttplate. (Some models have wooden and/or folding stocks.) This special purpose individual weapon is used for guard duty, prisoner supervision, local security, riot control, and any situation which requires the use of armed personnel with inherent limited range and ammunition penetration.
Background: Various models of shotgun have been in service use since 1901. The current inventory consists of four different 12 gauge shotgun models: Remington 870, Winchester 1200, Mossberg 500, and Mossberg 590. (Weight and length of the weapon depend on the manufacturer.)
They've been using shotguns for a long time (since 1901, above). Here's an example of an old Winchester, along with some of the newer shotguns currently in service with the US military, not just the marines.
Mark