In conventional warfare? The prospect of a civilian militia equipped with small arms managing to hold a candle against the sophisticated military technology, manpower and domestic intelligence available to the United States government is absurd.
However, this would never be a conventional war. The conditions that would justify such a scenario in a society such as the US would most likely also lead to the immediate fragmentation of government institutions, especially those that depend on the support of the public. Large portions of the government employed workforce and the resources they represent, even the top brass of the military, would be at risk of committing treason against the state and joining rebel groups, as we've already seen in current civil conflicts. In such a situation, the civilian side would not be headless, rather it would controlled by political and military forces, for it is inevitable that only one section of the political spectrum would benefit from this presumable breakdown of democratic rule.
The government is not the monolithic organization that appearances indicate, it is a complex network of social institutions that employ and require the complacency, if not trust, of the people. So if this war is to be fought, it would be done so under uncertain and chaotic domestic conditions against the powers that be and those on their payroll. This domino effect will level the playing field considerably until the victory of a civilian side becomes a realistic possibility.
There are many ways such a scenario could proceed and it depends on the involvement of different factors, such as whether the initial cause was ideological differences, degradation of civil freedoms, social/economic inequality, the establishment of classism or plutocracy and so on.
