I booked through priceline.com and was able to find a decent round-trip flight from Detroit to Los Angeles for around $400 plus accommodations at the Rodeway Inn just across the street from Television City for about $90 a night, if I remember correctly.
Since you're looking to just do it all in one fell swoop with no hotel, your best bet is to catch a late night flight out of Connecticut, say around 11:00 PM the night before or earlier, take a cab from LAX to Beverly Blvd. (depending on traffic, it'll probably take about 15-20 minutes or so), wait in line during the middle of the night, get your order of arrival pass at 6:00 AM, take a walk around downtown L.A. to kill some time, head back to Television City around 11:30 or so, get processed and see the show. (When I saw the show, I was in the audience for the second taping of the day, so, the audience was just leaving the studio as we were just finishing up with Stan, so, say around 3:00 or so). Take another cab back to the airport, board your return flight when it arrives, and call it a trip.
Of course, the tricky part is going to be finding a round-trip flight within a 24 hour span. If you can't, like I siad, the Rodeway Inn was a decent place to spend the night. Plus, they offer continental breakfast...some of the people I talked to said some of the other hotels in the area charged more and didn't give you anything.
You'll have to have some luck though doing it in such a short span of time...airplanes can be delayed...
