Hold semi-annual town-hall/fireside discussions with bi-partisan Congressional leaders. These discussions should be similar in nature to the fireside chat held on Google+ after the second State of the Union address (link to YouTube video below).
Through regular communication with the President, Senate Majority/Minority leader(s), and the House Speaker, major issues can be discussed and progressed through a medium that speaks in a more immediate fashion to the national constituency. It would also allow a more public and consumable debate between party leaders.
YouTube Video of Fireside Chat with President Obama:
http://youtu.be/kp_zigxMS-Y