The minimum temperature Danstar reccomends is about 62, so you wouldn't want it dipping too far below there. Fermentation generates some heat of its own, so in a 60F basement, as long as the fermenter isn't right on a concrete floor or anything, you're probably fine. It'll just take longer to complete fermentation.
You may want to rouse the yeast so ensure they don't completely fall out before they are done fermenting. I'd also look into getting a brewing heat belt or wrap and maybe putting an old blanket or jacket over the beer.