As opposed to static content / data?
There's a ton of variables in a question like this.
Server capacity.
Hosting company bandwidth
Proximity of the website host to the server providing the data. You may host in Chicago or Texas but the data might be hosted in Europe.
Backend programming language chosen.
Is the code requesting a json file or querying an SQL database? What kind of query are we talking about? A simple select email from users or a more complex join? Is the DB properly index?
How complex is the script being requested? Simple or is it processing images or working on data?
How often are you polling for data? Every 5 seconds or every 5 minutes?
How many concurrent users are making the same request?
Any dynamic site needs to get it's data from somewhere. Response times will come down to efficient code, thought out infrastructure and good sys admin skills to optimize servers. A Couple users on the site at any given time "shouldn't" be an issue. Thousands and that's why hosting companies have scaling solutions now.