at the very least
1. At or of the lowest amount possible; at the absolute minimum. Often indicates the belief that a greater amount is likely or should be considered. I know you don't have much money, but you should pay for your own dinner at the very least. The contractor said the repair work would cost $900 at the very least.
2. In any event; regardless; despite what else may have happened or is the case. I know you aren't interested in seeing this play, but at the very least we'll have a nice night out on the town. I know you don't see eye to eye with your father, but he's trying to maintain a relationship with you at the very least.