Final answer:
The term for the rapid surge in popularity of British bands like the Rolling Stones in the 1960s in the U.S. is 'British Invasion.'
Step-by-step explanation:
The 2-word term for the rapid U.S. popularity of bands like the Rolling Stones in the 1960s is British Invasion. This term describes the influx of British music and bands that swept across the United States during this era, epitomized by groups like The Beatles and The Rolling Stones. The British Invasion had a significant cultural impact, as it introduced new musical styles and brought about a greater appreciation for British music among American youth.