the president of the united states is not an economic advisory position, and the president has no proper role to play in the economy. that role is held by congress. the presidency is a military and foreign policy role, which is primarily about commanding the military.
the confusion that the british press may have about this issue would be related to comparing the prime minister to the president, but that is a false comparison. the prime minister's role in britain is quite broad due to the fact that the king has taken on a dignitary role. in practice, the prime minister is both the leader of the house of representatives, there called the house of commons, and the functional commander in chief, because the king holds no real power. in the united states, the president is not the leader of the house of representatives and does not hold the responsibilities associated with it, but is strictly a military and diplomatic role.
economic legislation is not written by the president but by the congress and the congress will rightly be judged on it's economic performance.
the president will be correctly judged on his foreign policy performance, as that is his role and his job in the american system.