For illustrative purposes let's say your div has id="d", then you could do:
var d = document.getElementById('d'),
dWider;
d.style.maxWidth = '9999em';
d.style.overflow = 'visible';
dWider = d.offsetWidth > 100;
d.style.maxWidth = '100px';
d.style.overflow = 'hidden';
Then the var dWider will be true if the text overflows and false if it doesn't.