Between two defenders
 

A1 gets the ball at the free throw line. B1 and B2 are right behind him, almost shoulder to shoulder with each other. A1 pivots and tries to get through the two defenders. There's contact by A1 on the defenders, but not enough to really displace them (however, it's a tight space). A1 has a clean path to the hoop should he get through them.

Charge or play on?

They need to hold their ground; chances are he's going to travel or trip or double dribble or something illegal. If they're that close and he gets through without displacing them, then they gave up their ground voluntarily.

It's very difficult for something like this to happen cleanly. File it under "have to see it." If nobody's displaced and he maintains control, play on. As snaq said, odds are in favor of the trip, lost ball, etc. I'll see that and raise you that he'll most likely give you a dirty look and expect you to bail him out with a call.

Does depend on what happens. Defenders have the right to be there and hold their ground.

By rule 10-6-2, this is a charge always. The dribbler shall not attempt to dribble between two opponents or between an opponent and a boundary, unless the space is such as to provide a reasonable chance for him or her to go through without contact.

Obviously there are no "always".:rolleyes:
You may want to argue no displacement if the defenders are a little farther apart and they back away. But according to the OP, they are nearly shoulder to shoulder and right behind the dribbler. In this sitch, there's not much chance of him going through without contact.
I'd go with the whistle.

If a guy is trying to thread a needle and the thread is too big for the eye of the needle, that guy isn't getting any help from me.

If they're that close (shoulder to shoulder), he isn't getting through cleanly. If they're "almost" shoulder to shoulder, it's very possible if he's a good enough ball handler. If they don't get displaced, then I've got nothing. But, OTOH, I'm not bailing him out, either.
Rule says the onus is on the dribbler here, not that it's an automatic foul.

Agreed. He might get through. If he doesn't, he's likely going to travel.