And that problem would be the military junta currently running the official government in the south. From Gallup:
'Malians' confidence in their governmental institutions plummeted in late 2012, as Islamist rebels took control over much of the northern parts of the country and after a military coup in March 2012 overthrew President Amadou Toumani Toure. Malians' faith in their national government fell 22 percentage points to 49% in November 2012, from 71% in 2011. Confidence in the military dropped 25 points and support for the judiciary declined 17 points.'
Nothing terribly surprising here, but public support for the military is worthy of note. Gallup data from as recently as 2009 showed Mali to be one of the most pro-American countries in the world, but much of that was likely wed to Malians' faith in their civic and military institutions. (Institutions the U.S. has heavily invested in over the course of the last decade, incidentally.)
Driving Islamist radicals out of Mali is obviously the West's priority at the moment, but it's difficult to envision a sustainable victory in Mali without a more accountable regime in Bamako.