I'm sure there are plenty of people that get away with putting big tubes in smaller tires. I wouldn't do it except as a measure to "get by" until I could get something better.
If the tube is too big at the get-go, then there will likely be some irregularities in the way the contact patch behaves as your tire travels over the road. You may or may not perceive this depending on how sensitive you are to such and how bumpy the road surface is itself. On the more extreme end, you might see bulges and depressions in the tire surface that may indicate wrinkling and kinking of the tube inside.
I'd err on the side of smaller tubes instead. However the smaller they are, I'd think the more they'll be prone to failure when something stick in them but doesn't completely puncture them.