The only likely solution is fuel cells. The U.S. Air Force has started using these to replace electricity generators in some of their bases. This is a field test of the technology, but if the fuel cell devices prove reliable, the U.S. Army will equip its troops with smaller versions of fuel cells. For example, the typical 30 pound load of batteries could be replaced with a six pound fuel cell (plus another six pounds of fuel.) The army is planning to use fuel cells that run off small cartridges of methanol, which are much lighter to ship, and carry, than batteries, and deliver much more electricity per pound than conventional batteries.
Soldiers are sometimes carrying more batteries than bullets into combat. For some infantry operations, especially those lasting 72 hours or longer, troops are required to haul up to 30 pounds of batteries. Special Forces are particularly hard hit by this, as they often have to go in by foot, to avoid detection, and set up a surveillance operation that consume a lot of batteries. This is very common in Afghanistan.
The lightweight fuel cells are expected to show up in the civilian market in the next few years. They will initially be expensive (several times the cost of a comparable gasoline powered generator), but the intended market, initially, will be backpackers, and the many soldiers who buy additional equipment with their own money. Shortly after that, the militarized fuel cells should be in service. This technology had been in development for over a decade, and is not considered likely to get derailed at the last minute with some unforeseen technical glitch.