I was asked some time ago to go and do some work on the other side of the world. Its awesome, I've been to the country a few times and really liked it and I enjoy the project and want to be involved. But there have been some funding problems and now they cant even pay for my travel costs. So Im basically going to have to pay loads of money to go and do the work. It will be really embarrassing if I let them down, its unlikely that they will find anyone else willing to do the work and my personal relationship with the team will be damaged. Ack! I'll be broke if I have to pay this!

I would be honest and explain that you would love to do the work but that your financial position is such that you can't afford to get there - surely no one can object to that?