Carpet or rubber floor mat?
For carpet, use an ice cube (put it in a plastic bag so it doesn't drip) and rub it on the gum until it freezes. Then, use a dull knife to scrape off the gum. Release as needed to get all the gum. If there is a stain afterwards, you might try carpet cleaner.
A search on Google led me to this link:
http://www.nacgm.org/consumer/unstuck.html
If it's a rubber mat, believe it or not, I've had really good luck with sticky stuff using olive oil (our exterminator told us about it and it really works!). Once the sticky residue is gone, then clean the olive oil with a degreaser (409 or Simple Green work well).
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