The United States has no choice but to adapt the skills and develop or acquire the technology necessary for asymmetric or "fourth generation" warfare if it wishes to survive in an unstable, multipolar, geopolitical world. The power of non-state actors has increased exponentially in recent decades. A better question might be whether American political leaders would use such an upgraded asymmetric capability wisely. Few of them have the experience or knowledge to do so, making the question difficult if not unanswerable.
The simplest definition of asymmetric warfare is conflict between two belligerents, one of whom is much stronger in terms of conventional military and economic power than the other. In the past, guerrilla tactics were often effective strategies for weaker forces who were fighting on their own terrain and therefore knew it better. This strategy has been seen with the Viet Cong in the Vietnam conflict and the Arabs under the command of T.E. Lawrence in WWI.
More recently, non-state actors such as Osama bin Laden and ISIL have demonstrated all too clearly how such opponents have incorporated huge advances in the technology of communications, cyber, logistics, weapons, and psyops (or propaganda) in the service of terrorism. Military historian and strategist William S. Lind, who coined the term "fourth-generation" warfare, uses the U.S. occupation of Iraq as a prime example. The best-financed, most powerful army in history was stalemated by impoverished terrorists using cheap improvised explosive devices (IEDs).
During the Obama presidency, the use of UAVs and other robotic systems for anti-terror purposes, a step in the direction of asymmetric warfighting, was seen as a mixed blessing. The practice has been both applauded for its efficiency and abhorred for its infliction of collateral damage.