Excel 2003 only supports 65,535 lines. Server memory will probably be an issue at some stage too.
The solution to your problem of too large an Excel file will depend on many factors.
You may be able to get more data into an Excel 2007 .xlsx file format, because this format is really a zip file containing a number of xml files. One of these files is a strings file which enables additional space saving by storing duplicate strings in your workbook only once (your wookbook just contains multiple subscripts). Rename an Excel 2007 .xlsx workbook as .zip and you will see what I mean. Excel XP and Excel 2003 users can view and update Excel 2007 workbooks if they download and install the free Office 2007 compatibility pack from Microsoft.
The other main issue to consider is why do you want to post large amounts of data on a web site? If your site is an intranet you might be able to generate large workbooks overnight in scheduled tasks rather than giving users fully up-to-date and online data. You may even be able to publish these workbooks on network shares rather than using a web server. Does all your data have to be in the workbook? Could you have summarised data in the workbook and provide detail files as appendices in other workbooks? You may even create an Access database for your users to download.
These are all issues I have encountered at work within the last year or two. Let me know if you want more information on these subjects...