They definitely will last, but here are a couple options to make sure they're the freshest and best.
1: Green Smoothie Bags
When you get home from the grocery store, wash and prep your greens and fruit - I usually chop off any stalky stems from kale, chunk up any greens, and either put my ingredients into big individual ziplock bag or make "smoothie bags" that include several of the ingredients I'm going to use in my smoothie during the week.
I don't always pre-chop the fruit, as it can get a little sticky in there and is always more fresh when you cut into it just before you're going to blend, but doing this a day or two in advance is absolutely fine.
2: Freeze Smoothies
Pre make your smoothie and freeze it in ice cube trays. This will lock in the nutrients at their freshest and best right after they're blended and cut up, and you can throw them in the blender like ice cubes first thing in the morning.
You can also try having your smoothie either for breakfast, or as your first snack so you can drink it fresh. Of course, if this doesn't work for you, you can store it in a refrigerator to drink later in the day. The only thing I warn against is pre-blending smoothies days in advance. At least make sure you blend the smoothie the morning you will be drinking it.