Most everything you're studying as a historian has been over and done with for a long time, so it's not like there are going to be any sudden historical emergencies. That doesn't mean this is a stress-free job, however.
In the course of your career, there will be a lot of paperwork. You'll have deadlines to meet and papers to publish. If you're a research historian, some of your ideas may very well get challenged by other rival historians—competition is more of an issue in the world of academic history than you might think. Also, international travel will come with its own special brand of organizational headaches.
Historians who teach have busy schedules. A typical day for a history professor may include developing a lesson plan, grading papers, being available during office hours, and dealing with editors. And that's not even to mention their actual job—teaching the classes and researching their various projects.
The upside is historians do have pretty flexible jobs, which allow them some family time. You may have a lot of work in front of you, but history generally stays where it is while you play with your kids and get some shut-eye. Don't worry, the ancient Jordanian ruins will still be ruined tomorrow.