This can and has backfired before, though. Top teams don't look to change up the room by making a splashy trade. And a pre-deadline acquisition of a top 6 C is very "splashy."
Add to that, with NHL parody (artificially contrived or not), outside of San Jose, Anaheim, Chicago, and Ottawa (maybe CBJ, too, but have to image the Jarmo gets fired when the season is over, and sending the message that it's "over" 35ish games in is a surefire way to get canned), no one is going to be selling for anything short of major premiums.
So unless you see something on one of those rosters that is so enticing that the Rangers should pay a premium to get right now, there is no move to be made. For the record: I don't see anything on those rosters that would be available that I'm paying much at all for, forget a premium, and no top 6 Cs.