Temporary visitors visa extension.

Is it possible for an american citizen to have there temporary visitors visa extended for another 90 days in Japan?

Not under usual circumstances. But I suspect you could get an extension with a really good reason.

Do you think marrying a girl that I love who just became a Japanese National so that I can apply for a spousal visa to stay there with her would be a good reason for an extension?

It would depend on the Immigration officer making the decision. Head out to the Immigration office and ask.

Do i have to apply for a spousal visa in my home country or can I apply for it in Japan after we have already married? We want to have our wedding in Japan when she becomes a national and I was hoping I wouldn't have to go back to the USA just to apply for the visa.

See here:
http://www.japan-guide.com/forum/quereadisplay.html?0+44780

So I would have to leave once while waiting for the certificare of eligibility. If she was willing to be a gaurantor for me is it possible that my status of residence could be extended, rather then leave Japan once?

Again all I can say is it would be a case by case specific decision by immigration authorities.

If you have her or better yet her family back you up it is possible, but I would go down to Immigration as soon as possible and just ask.