Edit in JSFiddle

var App = Ember.Application.create();

App.ApplicationController = Ember.ObjectController.extend({
    message: 'This is the text that should be copied'
});

Ember.Handlebars.helper('zeroClipboard', Ember.View.extend({
    tagName: 'button',
    classNames: ['btn'],
    attributeBindings: ['title', 'data-clipboard-text'],
    title: 'Copy to clipboard',

    didInsertElement: function () {
        var clip = new ZeroClipboard(this.$(), {
            // This would normally be a relative path
            moviePath: "http://coderberry.me/assets/ZeroClipboard/ZeroClipboard.swf",

            // Added for demo on JSFiddle. See http://goo.gl/DLl7O
            trustedDomains: ["*"],
            allowScriptAccess: "always"
        });

        clip.on('complete', function (client, args) {
            alert('Copied "' + args.text + '" to clipboard');
        });
    }
}));

<script type="text/x-handlebars">
    <div class="container">
        <div class="input-append">
            <span class="span4 uneditable-input">{{message}}</span>
            {{#zeroClipboard data-clipboard-textBinding="message"}}Copy{{/zeroClipboard}}
        </div>
    </div>
</script>