It depends on the laser power. I can't speak for the US, but here in the UK a class 2 laser is considered safe as you're blink reflex will kick in before any damage is done. This equates to about 1mW. If you look at the laser swamp kits from frightprops, the smallest power they sell is 50mW.
These lasers don't use scanning mirrors to make the line, they use a glass lens meaning the beam is constantly on and not scanning, having said that the power is spread out over the width of the beam. At that power eye protection is recommended, but this is normally avoided by having the swamp line lower than eye level reducing the risk of someone looking directy into the beam. You can also think about the placement of your lasers so as to reduce the risk, but it's worth noting that a laser directly in front of you will appear birghter than one to the side or behind.
Every space is different so you will need to do your own risk assessment for your space. Realistically are you going to have any injuries? Very unlikely. Is there a chance? Yes. You just need to make sure you've done all you can to protect your guests if you go ahead with it.
Things to keep in mind:
Keep out of eyelines
Front on lasers appear brighter
Green lasers are the brightest to the human eye (you can use a lower power green laser for the same effect)
Do a risk assessment. You may decide having a warning not to look in to beams before they enter your attraction is sufficient.