our flight departs at 7 am from dtw to cancun mexico on sat nov 9 what time should we arrive at the spirit cunter at airport?

Be at the airport and standing in line for check in by 5:00 AM. If it was during a busier time of day then you should make it 2 1/2 hours since DTW is a large airport. 

You should be at the counter at least 2 hours prior to departure. I have found it best to be at check in counter 3 hours before departure. Line ups can take time to get through, and then you have to clear security. If you do get through early, you can get a cup of coffee and something to eat while waiting for your flight departure.

The general guidleline is that for larger metropolitan airports such as Detroit that you arrive two hours before you flight is scheduled to depart.

I realize this can be a nuisance because you might breeze through security and wait at the gate for an hour but it certainly beats the alternative of missing your flight. 

Your ticket should have the arrival time on it.