You'll be okay unless it keeps raining and it stands for a longer time than this.
Mulch will help, btw, because when water stands like that, if you have any clay, it tends to turn the surface of the soil into a rock. Mulch prevents this somewhat. But now you know for next year to add some soil or do some leveling or create a waterway for runoff.
I think you'll be okay if it hasn't been standing any longer than that.
It'll be obvious if the plants start to get waterlogged. They'll start to turn kinda sickly looking and wilt.
If it doesn't drain, though, you'll need to get out there with a hoe and create a little ditch to get it to run off. Also, you can hill up the soil around some of those plants so the area around the roots will drain a bit better than the surrounding area. Lots of little tricks. If they're already mature though, you might not have too much luck with emergency measures this season.
Let us know how it turns out.
Kitties