President Barack Obama’s jobs council is disbanding Thursday, two years after the president tapped top executives from General Electric Co., American Express Co., Boeing Co. and other companies along with labor leaders and academics to advise him on steps to spur employment and economic growth.

For a president who has had a shaky relationship with the business comminuty–and particularly Wall Street–the council gave him some political cover from Republicans and business leaders who criticized his administration for enacting tough new regulations. In recent months, however, the council had become a political thorn as Republicans accused Mr. Obama of ignoring it.

The website for the President’s Council on Jobs and Competitiveness, as it’s formally called, shows it met four times since its inception – the last time on Jan. 17, 2012 — and held 18 “listening and action sessions” around the country with businesses and local leaders…