2 years late...but I wound up here looking for an answer to the same question. Eventually got it figured out, try something like this:
<style>
.embed-container {
position: relative;
padding-bottom: 56.25%;
height: 0;
overflow: hidden;
max-width: 100%;
}
.embed-container iframe,
.embed-container object,
.embed-container embed {
position: absolute;
top: 0;
left: 0;
width: 100%;
height: 100%;
}
</style>
<div class='embed-container'>
<iframe src='http://player.vimeo.com/video/66140585' frameborder='0' webkitAllowFullScreen mozallowfullscreen allowFullScreen></iframe>
</div>