Why are my jaw muscles suddenly going tense?

Could be stress. In today's society, many people are finding themselves under more and more stress. The body often reacts to this by clenching or grinding the teeth. Since the muscles of the jaw are like any other muscle, the more they get 'worked', the larger and more powerful they can become. This will lead to more tension, force, and possible pain and joint problems.
Likey TMJ disorder. It sounds like you are experiencing temporomadibular joint disorder. This disorder can come and go throughout a lifetime or become constant. Signs of tmd are pain in the jaw, ear aches, headaches, popping and clicking, and can cause your jaw to lock. This condition is usually brought on by stress, however can develop overtime if your dental bite is not properly aligned. I suggest a prosthodontist.
Stress, TMD. Could be clench/grind your teeth secondary to stress. Can lead to TMJ problem. The time of day you notice this is important. If you wake up with tense jaw muscles, likely nocturnal bruxism. If daytime, then during the day. "Teeth apart, lips together" when not chewing or talking.