IF a trade did happen, then I do think that Miller would be a long-term fit into the rotation. That's a big if though, as I can't really think of anything in particular the Tigers need other than another setup guy to go with Zumaya/Rodney.
If not, he could go as few as one game, probably depending a lot on performance. If he doesn't pitch well his first time out, Leyland won't have any problem going with Zach Miner (already on the major league roster for Zumaya, in the bullpen). Miner started the majority of Maroth's starts last season after his injury, pitching very well, and has been respectable this year as well. Long-term, unless someone does get traded, this is going to be Roger's spot in the rotation, as it doesn't look like Durbin is going to be giving up his anytime soon.
Frankly, I'm not sure why Miner isn't getting the start in the first place. He did put in some extra work this past week, mostly because of Robertson's poor game, but he'll have plenty of rest going into this weekend as long as Leyland doesn't use him tonight.
Miller is certainly in the future for the Tigers... but until Dombrowski clears some room for him, nobody's really sure when that future is going to be.