As the folks above mentioned this is called hidden city ticketing and has some concerns and pitfalls. You also run the risk that during IRROPS they route you via some other connecting city to your ticketed final destination so you'd no longer be going to the place you intended to skip off. You're then left finding your own way at additional expense to your real destination.

As noted above this question comes up weekly, if not daily lately.

Have you looked at Southwest? Their flights won't show up in online sites like Orbitz you have to go direct to their website. Over half a dozen daily non-stops between MSP and MDW (Chicago Midway). They're no longer the "el-cheapo" they once were but always worth a look.

If you really want to do it as cheaply as possible, are on a leisure trip without schedule concerns (especially due to current delays on the route), you can do St. Paul to Chicago Union Station on Amtrak. Currently $66 or less one-way in coach, ~8 hours each way, maybe longer if delays haven't cleared up yet.