Very messy...looking at a near worst case possibility
I suspect that anyone that shoots at the troops gets a bad case of dead really quickly. These guys are the best. Of course, there might well be noncombatant deaths. They were more realistic about that back then...people tended to understand that, when bullets fly, they're adressed to occupant. Even so, a lot of outrage against someone...whether it's against the troops or the terorists is hard to tell.
And with the governor opposed to the desegregation, what dioes he order the National Guard to do when shooting starts? For that matter, what does the guard commander on the spot do? I feel confident that the local guard commander was anti desegregation, since the Governor sent the force to prevetn integration.
Worst case, a pitched battle breaks out between the National Guard troops and the US Army. In OTL, the guard had been federalized and ordered to return to their armories...but what if Governor Fabus had told them to stand fast, and they had obeyed the governor rather than the Federal Government. I don't see Eisenoower waiting any length of thim to argue the case.
Even if a battle doesn't break out right then, it's a bad situation if the KKK starts attacking other federal targets such as tax offices. Is there anyone that could calm the situation down? Or does martial law get declared throughout the state?
And absolute worst case possible, Eisenhower goes before Congress and declares that Arkansas is in armed rebellion against the United States...