Have a look at dayRender()
method. I know... There isn't that much documentation... Here is a working fiddle of how to change the background color of the current date and all the 7 days after current date using this event:
$(document).ready(function(){
$('#calendar').fullCalendar({
header: {
left: 'prev,next today',
center: 'title',
right: 'month,basicWeek,basicDay'
},
defaultView: 'month',
dayRender: function (date, cell) {
var today = $.fullCalendar.moment();
var end = $.fullCalendar.moment().add(7, 'days');
if (date.get('date') == today.get('date')) {
cell.css("background-color", "red");
}
if(date > today && date <= end) {
cell.css("background-color", "yellow");
}
}
});
});
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script>
<script src="https://cdn.jsdelivr.net/momentjs/2.10.6/moment.min.js"></script>
<script src="https://cdn.jsdelivr.net/fullcalendar/2.0.1/fullcalendar.min.js"></script>
<link href="https://cdn.jsdelivr.net/fullcalendar/2.0.1/fullcalendar.css" rel="stylesheet"/>
<div id='calendar'></div>
Have also a look at moment.js documentation in order to manipulate the date objects.
EDIT
I assume you're using fullCalendar v2. For v1 have a look here and here