Americans are losing faith in the value of a college degree, with majorities of young adults, men and rural residents saying college isn’t worth the cost, a new Wall Street Journal/NBC News survey shows.

The findings reflect an increase in public skepticism of higher education from just four years ago and highlight a growing divide in opinion falling along gender, educational, regional and partisan lines. They also carry political implications for universities, already under public pressure to rein in their costs and adjust...