If the US had to assault a beach today, the assault would have to be conducted from over the horizon in order to avoid being targets for anti-ship missiles launched from several miles inland. This would push amphibious ships back approximately 15-20 nautical miles, stretching the range of current AAV range, which would work in conjunction with assault aircraft and helo's. Factors to consider are sea state, enemy defenses, maneuverability of nearby enemy armies, range of landing craft, potential casualty rate, availability of logistical support upon landing etc. All of these factors come into play when launching an amphibious assault, and each and every factor has an acceptable "failure rate", which may or may not become a limiting factor with respect to launching the assault.
The actual assault would have a long timeline, and would look something like the following:
0100: Begin aerial and missile bombardment
Photo: US Navy Photographer's Mate 3rd Class Laura A. Moore