I don't know what you are talking about with a long line for a teller. Ever since ATMs were introduced (years ago), there have been long lines at all ATMs and no lines at any of the bank tellers that I use (and I use at least 7 branches of 3 different banks). I walk right past all the fools at the ATM and get done with my banking faster, with personal service, and no possibility for an ATM fee. Of course, I use good banks which have tellers for at least 8 hours on Saturdays, have tellers open on Sundays, and have tellers late in the evenings. Your bank must suck.
To answer your question: they won't pick up the ATM deposits until this evening. They won't process it until tomorrow. That brings the real question. Does the check expire on the 29th or AFTER the 29th. I cannot answer that question. It may not be a banking question, rather a question regarding the company that wrote the rebate check. Save yourself the trouble and just go to a teller before 3 pm today so you know it counts as a transaction today. Or, go deposit it for cash at some place like Walmart where you don't have an account. It'll cost you a buck or two, but you'll never have to worry about the expiration.