So, I missed my 6 AM flight out of LGA to ATL today (was at the gate at 5:50, flight was closed). They put me on standby on the next flight, which got me to ATL about 5 minutes before my original connecting flight to CMH. The next CMH flight isn't until 9 PM. But I'm only standby on that flight.

My question is -- once AirTran takes me to my connection point, do they then have an obligatory duty to get me to my final destination? I understand that it was my fault for missing the first flight, but by flying me to ATL, they have taken the obligation of getting me to my destination, right? In other words, can I demand that they give me a confirmed seat for 9:00? I'd hate to have spent 11 hours in ATL only to not even get on this flight.