Individual phone carriers have daily limits. T-Mobile, for example, has a limit of 1,000 messages per day from a particular organization. Assuming your messages are distributed equally among the major carriers, a likely daily limit is 3,000 messages. This is an estimate, not a hard limit.
Important Note: Billing for the Text Messaging service is separate and different from the billing for your WildApricot subscription plan. You must apply for a Text Messaging account and provide credit card billing information for that account. Text Messaging is not bundled with any WildApricot subscription plan.