I would push them for an official admission offer in writing BEFORE you commit. They haven't actually made an offer for you to commit to so why should you commit. If it were me, I would tell them, I am very interested in their program, but I cannot consider it until an official admission offer is made. That's even before a funding discussion takes place. Then I would tell them I need some time to think about the admission offer. Because worse case scenario is if you really think you are committing even though nothing was ever in writing or official and they can't find funding - where does that leave you?
Another option you have which is more underhanded on your part is to commit and then pull out yourself if you want to. It's the 'underhandedness begets underhandedness' approach. That won't eliminate other offers but make these people come forward with money. Then if you back out you can use their lack of putting an official offer in writing against them. It's not really a commitment because you never had a real offer. You are just giving them the go ahead to get funding. I don't think its a big deal if they allocated money for something and then you said no. The money as long as it wasn't physically transferred across departmental lines will go right back to where it came from.
Unfortunately, we are not in a position to do much negotiation when lots of people can fill our spots. Unless we are the people they absolutely have to have if we don't play their way, they'll just replace us easily. Doesn't it all come
back to the law of supply and demand or something?