rjw0501, that ISN'T recommended.
What browser do you use? Do you have ANY other protection programs than SpySweeper and Norton?
If you would disable both of them-- then surf few days - then clean with them, my opinion is NO. You could get whatever malware/viruses - Norton can't clean your system by itself.
Or if you REALLY wan't to disable it (and as I said - it isn't recommended),
you should download at least SpywareBlaster here; http://www.javacools...sbdownload.html
(Small program - won't take resources much - is freeware - has excellent protection & you don't have to keep it opened to get the protection.)
Update -> enable protection.
If you're using Internet Explorer - then it would be absolute NO to disable protection.
Get Firefox - http://www.mozilla.org/
Don't tell me that you don't have a firewall?
And, if you're trying to get rid of your protection because your computer is SLOWER - I would say it isn't a good excuse. Since if you would get bad infection.. Let's say like browser hijack, then your slow computer would be last of your worries.