JSFiddle - React, Tailwind, and code Playground
HTML
<script src="http://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/2.1.0/bootstrap.js"></script>
<link rel="stylesheet" href="http://getbootstrap.com/2.3.2/assets/css/bootstrap.css">
<button class="btn" id="btn">Click Me</button>
<div class="modal hide" id="modal" tabindex="-1">
<div class="modal-body">
<input type="text" id="datepicker" />
</div>
</div>
JavaScript
$("#datepicker").datepicker({"changeMonth": true});
$('#btn').click(function() {
$("#modal").modal('show');
});
$('#modal').on('show', function () {
$.fn.modal.Constructor.prototype.enforceFocus = function () { };
});