I don't use SMB much yet (wireless network is sooo slow), but in normal pathnames you can use a space by 'backslashing' it. Maybe you have tried this already, but just in case. (note the extra slash after 'the').....mmmm I'm starting to feel a bit dumb with this one. It could work I suppose if you could use forward slashes (I changed the slashes around to illustrate) in the rest of the path.... nah maybe try the second idea.
mount -t smbfs //ComputerName/The\ Share /mnt/share -o username=somebody password=something.
stick in a %20.... hey it's just an educated guess, worth a quick shot though.
mount -t smbfs \\ComputerName\The%20Share /mnt/share -o username=somebody password=something.
note both of these guesses are HIGHLY speculative.