In my communicative environment, the expression
Du hast wohl einen an der Hacke
is used to express doubt about somebody's mental health, or simply: "You seem to be a fool". However, as Mr. Schulz used it
Jetzt haben wir erst mal richtig was an der Hacke
it would rather mean "Now we have a big problem", or "We have taken a big defeat".
About the origins of the expression, or how Mr. Schulz understands the words and wires them in his mind, I would suppose Hacke is the heel, and "to have something at the heel" could be an euphemism for having stepped into a heap of excrement part of which now sticks to the heel. This at least would fit the situation his party, SPD, is in now after their unfavourable results of the elections in the province of North Rhine-Westphalia (May 2017).
A less "smelly" origin of the expression could be: you are walking through a wet, muddy field and the dirt sticks to your boots making them heavy, so walking becomes difficult. This would fit SPD's situation as well.
See, however, Takkat's historical etymology in the other answer posted here on this page. In this light, my "personal" etymology reflects only a contemporary state of mind, and the expression seems to derive from an idiom coined by people engaged in fighting and physical persuing opponents.
For those who are learning German: you can use both expressions with your friends or family or in the pub after two beers, but you should not use it in more formal settings e.g. at work, with superiors or whereever politeness is advisable.