You must use cake naming conventions for form elements.
For example, if you call $this->input('Model.field', array('type'=>'date')) in the view, the generated html-selectboxes have the following identifiers: #ModelFieldMonth, #ModelFieldDay, #ModelFieldYear .
So, the code to get the full date in JS:
var date = $('#ModelFieldYear').val() + '-' + $('#ModelFieldMonth').val() + '-' + $('#ModelFieldDay').val();
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