We mopped up the water — since it was just plain water, it wasn't particularly messy, just wet — and vented the remaining water from the washing machine into an empty plastic trash can, which I relayed (it took several trips) to the adjacent bathroom and poured down the toilet. At least the toilet drains properly. We'll have to call the plumber and have him back in next week so he can fix the laundry drain as well. We were both surprised that this hadn't been tested earlier.
I guess we're not yet rid of having to take our dirty clothes to the laundromat.