This is possible. However depending on the specific details - it may be fairly simple or extremely complicated. Here's how I imagine it working - you can extract the info from the spreadsheet - display those fields on the web - have users edit them - and then insert those fields back into the spreadsheet .. it's not exactly editing the spreadsheet live on a website but it accomplishes what you are looking for.
Here are some questions -
1. Does the data have to be stored in an excel spreadsheet? How about a database or text file? (it becomes simple if your not using a spreadsheet)
2. How many rows of data are you looking to display/edit at one time?
3. How many columns of data are you looking to display/edit at one time?
If you can work without a spreadsheet (I can put the spreadsheet in a database and provide dumps of the database which you can easily import into a spreadsheet for later use) then you can contact me via
http://buildacom.com (use the contact form). Otherwise - it's too complicated so I'll pass... besides - it will cost you a fortune compared to using a db.