We've been using Basecamp for about a year now. One of the API functionalities that is exposed through Basecamp's API is the ability to get a time report for a user (or for all users if no user_id is specified) for a specific time frame (or for today if no start/end dates are specified). This makes it really easy to then write your widget or web page to manage time entries.

Right now the the only way I can do this is 1) to directly access the database myself to retrieve that information or 2) to loop through every project and do separate API calls to get the time entries for that project and then manually filter out ones that aren't related to the user(s) or timeframe that I want. It's very tedious and heavy on the number of API calls and DB access.