Though it sounds like the plot of a movie the reality is that select Army engineers, Special Forces, Navy SEALs, and select Marines were once trained to employ backpack nukes.
The scientists of Los Almos Scientific Laboratory created the W54 atomic warhead in the late ‘50s. It was one of the smallest nuclear warheads ever fielded at under 11″ diameter (270 mm), about 16″ long (400 mm) and a little over 50 pounds (23 kg). The fuse allowed for one to select a yield from a tenth of a kiloton to a full kiloton. The W54 was also a pretty dirty bomb. People out to a quarter-mile away were likely to receive a deadly dose of radiation.
About 400 W54s were built. The Air Force employed some on AIM-26A Falcon AAM and the AGM-45 Walleye ASMs (to take out Russian bombers and subs, respectively). The Army employed them on the M-29 Davy Crockett, a jeep-mounted recoilless cannon tactical nuclear weapon with about a 3 km range. That left a couple hundred to be used by SOF as the MK54 Special Atomic Demolition Munition or SADM. The SADM was designed for a time where the US saw tactical nuclear weapons as a cheap and easy way to make up for capability.
The SADM had a combination lock covering its mechanical timer, which was EMP-proof, mounted in a shockproof case that was waterproof to 200 feet, packed onto a padded ruck. Total weight of the SADM was a little over 160lbs.