The Rangers will have to clear both a 25 man and a 40 man roster spot to make room for O'Day.
The bullpen doesn't have any obvious candidates to be dropped (and I have to wonder if the Rangers wouldn't have held off on calling up Derek Holland if they knew this was coming). C.J. Wilson and Holland are the only players with options remaining, and I can't see either of them being optioned at this point. (It was pointed out in the comments Willie Eyre has options, and could get optioned, although you'd still need to clear a 40 man spot)
It seems more likely that either Kris Benson gets designated for assignment or put on the d.l., Scott Feldman gets designated for assignment, or Vicente Padilla goes to the d.l. And if it is a d.l. move, you're going to have to drop someone currently in the minors off the 40 man roster.