They have paid out some already, I remember hearing about it on the news -

[BP has said consistently that it will pay legitimate claims for loss and damage caused by the spill. BP remains fully committed to responding to and paying claims promptly. To date, more than 26,000 claims already have been submitted, resulting in payments exceeding $36 million. ]
http://www.bp.com/genericarticle.do?...tentId=7062448