It depends on the state. Some states tax services (eg Ohio), while most states only tax physical goods.

So it would depend on the state that your SaaS company is located in, or where your customer is accessing it from?

The latter. If you are a SaaS business in a state that taxes services, you only have to collect sales tax for customers in your state today. Under the new legislation, all SaaS businesses in the US would have to collect sales tax for any jurisdiction that taxes services.

The simplest way around this would be to set up your SaaS business in Canada.