The law in question is the FRPAA (Federal Research Public Access Act), and it's a very fine thing: see http://svpow.com/2012/02/10/d-day-going-on-the-offensive-ove... on its importance and http://www.taxpayeraccess.org/action/FRPAA2012.shtml for more details.

The current petition is a different strategy towards the same goal, approaching the Whitehouse directly in the hope of catalysing a presidential-level directive that would jump-start the process. (Not a speculative hope, either -- relevant people have the ear of Obama's scientific advisor.)