Shawn,
That message is indicating that your site is running out of memory. I'm assuming you're just seeing this when you enable JFBConnect, but I don't think JFBConnect is necessarily the cause.. just what's exposing the problem.
Some information you could provide would be very helpful:
1) Let us know how much memory your website is allocated. If you go to Help->System Info and then "PHP Information", search for memory_limit. A good minimum number is about 16M. More is always better. If it's less, that's really low for running a Joomla site with multiple 'powerful' extensions on it.
2) Enable Debug Reporting. You can do this in Global Configuration -> System Tab. Enable "Debug System". At the bottom of each page, you'll see a report on how much memory is being used, as long as how many queries are on a page and how long it took to render. Lower numbers in all these areas is good. If you can, disable whatever is necessary to just make the site work, and let us know those numbers. If you're bumping up close to the memory number above, then enabling any other 'big' extension would cause the memory issue.
3) Try seeing if there are any plugins/modules/components you're not using on your site, but are still installed. While many, if unused won't 'do' anything and use memory.. some do, and it also just helps with the cleanliness of the site.
Hope this helps get you started, but if you can answer the above, I think we can help you diagnose the problem further and hopefully come up with a good resolution. If you're on a very cheap hosting plan, this may simply be an indication that you need to upgrade.
Good luck!