Let's look at the reason for that drop. The Republicans would like to think it is because more people now oppose the president's economic policies -- meaning more are now starting to accept the Republicans attempt to keep imposing their failed "trickle-down" policy. That is just not true. The poll shows the disapproval of the president's economic policy has remained constant for at least a year now (at 40%-41% approval and 53%-55% disapproval). That means the president's recent drop in job approval is NOT because of economic policy.
So what has caused the drop? Note in the top chart above that for the first time more people disapprove of the president's foreign policy than approve. It is this change in foreign policy approval that has caused the overall drop in the president's job approval rating. And that same chart gives us a clue as to why.
Note that only 33% of the public approves of the president's policy toward Syria (especially his recent decision to involve the U.S. in that civil war by arming the rebels -- which is supported by only 27% and opposed by 59%). Approval of the war in Afghanistan has also dropped (from 50% approval-41% disapproval to about 46% approval-45% disapproval), but that doesn't seem to have been nearly as unpopular as the president's actions regarding Syria.
But this doesn't help the Republicans at all. They are the ones pushing for more involvement in Syria (and other countries like Iran), and some would like to see the military more involved in Syria -- using either air power or ground troops. The GOP foreign policy desires are clearly at odds with the views of the American public.
Further proof that the Republicans are still losing the economic argument with the public lies in the second chart above. When people were asked whether they trusted the president or the congressional Republicans more to fix our economic problems, about 44% trusted the president more while only 38% trusted the Republicans (a difference significantly above the margin of error).
And that is not the only bad news the poll had for Republicans. A majority of the public still considers the president to be honest and trustworthy (50% to 44%), think he has strong leadership qualities (52% to 46%), and think he cares about the needs and problems of people like them (52% to 45%). I doubt any of the leading Republicans could score that high in those categories.
While the small drop in presidential job approval should worry the president (and cause him to rethink his policy on Syria), it should not be viewed as happy news for the GOP. The drop was caused by foreign policy moves -- moves the GOP supports (and would probably even exacerbate). The people still prefer the president on economy issues -- the area where the GOP is trying the hardest to win support.