A PhD thesis without any publication
This sort of thing varies by field. In some, there is no expectation at all of publications prior to finishing the degree. I think the push toward requiring publications is somewhat recent. When I finished (long ago) in mathematics it would be very rare to have any publications at all upon graduation. 

But in some fields there is such an expectation. However, I think that in those fields, students are funded more for research (RA) than for teaching (TA). If you are part of an active research lab in the sciences it is more natural to have several publications as a consequence of your work prior to graduation. 

But any effect at all on your career would likely be very brief. You establish your own reputation. Starting a bit late with publications eventually evens out if you are productive, either in academia or elsewhere. 

Of course, it won't harm you to be thinking about what you could get out there in your time remaining. Your advisor should be able to tell you about norms in your field, of course.