Frankly I don't know. One of the main problems is that the middle form biazetai can have either active or passive force.
Moreover, the interpretation depends on the context, and there are at least three possible contexts for this saying (Q, Matthew and Luke):
In Q (= Luke 16:13,16f):
No slave can serve two masters; for a slave will either hate the one and love the other, or be devoted to the one and despise the other. You cannot serve God and wealth.
From the days of John the Baptist until now the kingdom of heaven has suffered / exerted violence, and the violent take it by force.
The law and the prophets were in effect until John came; since then the good news of the kingdom of God is proclaimed, and everyone tries to enter it by force / is forced into it.
But it is easier for heaven and earth to pass away, than for one stroke of a letter in the law to be dropped.
But even this apparent context may be misleading, as the three sayings do not necessary belong to the same strata of Q (Kloppenborg, for instance, believes that the mention of the law in v. 16f is late).
The general impression I get in the context above is one of radical urgency due to the current lack of authoritative references (the law and the prophets), something like "now each man for himself" -- which would fit well with the rupture of family ties in the wider context. This would imply an active reading of biazetai. However, what follows (the law will not pass away, with or without the example case of repudiation in v. 18) seems to temper it somehow.
Now there may be in this saying and others, upstream of Q, a distinct tradition about a "violent Jesus", as Eisenman believes. Who knows?
I'm afraid it doesn't help a lot...