ClickyClack

I am also the ward building coordinator, and have been for nearly four years. There have been times when it has been quite a struggle for me, seeing how many people will completely trash the building, yet how few will show up to clean it. It is astounding how many people are willing to show up and use the meetinghouse, but are not only unwilling to clean it, but are unwilling to even clean up after themselves. And it is also astounding the sacrifices I have seen from people who are WILLING to come clean, in once case even when the gentlemen could barely walk from terminal cancer.
I once mentioned that to an older gentleman in my ward, and he told me that back when the church paid someone to clean the meetinghouse, he took that position while he was in college. He has since been bishop and many other things, but being the building cleaner was the hardest thing for him to do.
Furthermore, in preparing a priesthood lesson on sacrifice, I asked three bishops and former bishops what jobs or callings were the hardest to get people to accept. All three of them listed "ward cleaning" as the first.
So... how to do it? Well, take everything with a grain of salt. But here is how we handle the cleaning: At the start of every year, the bishopric makes a list of families to clean each week, including a "head family". It is not a suggestion, it is not a request, it is an assignment direct from the bishopric, so if people have any complaints, I can tell them "Take it up with the bishopric."
Each week that we clean, the head family is responsible for calling all of the families under them, letting them know, and coordinating a time to do it. I give them a couple of weeks notice, and let them know (gently, I hope) that THEY are responsible for the cleaning, not me, and that their best bet to get it done quickly is to get as many of the families under them to come as possible. I also tell them that if they (the head family) cannot do it that week, THEY can trade with another head family, but it is their responsibility. I also tell them that if one of the families under them can't come, it is that family's responsibility to trade with someone else. Like I said, it isn't a suggestion, a plea, or a request, it's an assignment that they can't get out of.
I then call them a couple of times in the duration leading up to the cleaning, and ask "How has it gone with the other families?". It helps them remember, and lets them know that someone is, indeed, checking up on them.
Now, the secrets of creating "The List": All of the head families are assigned from a group of families that are very responsible. As for the rest of the ward, they are divided into three groups: "They probably will come", "we don't know", and "they probably won't come". Each week's assignment is created of a mix of all of those three groups. Those people also include less active and inactive members, give them an opportunity to sacrifice and earn blessings as well. We have people who WILL NOT come to church, but will come EVERY TIME to clean the building.
So, as a recap: Make a good list, and make it the people's responsibility to perform the calling and work. You are the coordinator, not the janitor. I got lazy once, early on, didn't call anyone, and ended up cleaning the entire building by myself. I learned my lesson with that, and it won't happen ANY MORE. In fact, last month, a head family seemed to have just "forgotten" to do anything, so I kept calling all day long, and finally got ahold of them at about 10:30 at night, and asked if they had forgotten about cleaning the meetinghouse. They hustled their entire family over, and got it cleaned nicely!
Our stake president is very picky about the appearance of the building. If he shows up on Sunday at 6:00 AM and the building isn't clean, HE will clean it himself. Needless to say, that does NOT look good for the coordinator in charge. One Sunday, I showed up to unlock and turn on lights, and the cleaners (a different ward) hadn't set anything up. He looked right at me, and asked "ClickyClack, was yesterday your week to clean?" When folks really drag their heels at cleaning, I casually relate that to them... I think that a lot of people don't realize how dirty the building can get, or that people DO notice...
Now, one reason why *some* people don't clean: A lot of the older members grew up with the program where a paid janitor cleaned the meetinghouse, and they still aren't even aware that it is now the members' (and their) responsibility.
BTW, you have more responsibilities than just the cleaning (and locking up). You may already be aware of that, but when I was called, I wasn't aware of them for some time.
Another method that I've implemented is creating a sheet with all of the jobs, listed on "pull-off" tabs (like signs on the street) that the head family can pull off and hand out to those who come, to get them rolling faster. I also show up a little bit early and get out all of the cleaning supplies, so that the cleaners can just jump in and start. With a good crew, we can knock out the entire building in as little as 20 minutes.