You will need to have a table called Employee Dates where the Key field is a concatenation of the [Record ID# of Employee] and the [Date].
List("-", ToText([Record ID# of Employee], ToText([Date]))
If you like you can actually create the formula field and make it the Key field by using the API_SetKeyField&fid=10 API typed into the URL bar.
Then set up an Action to ensure that for every time entry, the action will fire if the Key field does not exists already for that Employee and date.
I do that by making a field Key field exists? with a formula value of true and look that up down to Time Entries, and fire the Acton of the Ket does not exists.
Then you will be able to make summary fields up to that Employee Dates to have the data available to know how many entries there were that date.
