Is it reasonable that a contractor has asked for two-thirds of the project cost by start time?
It could be worse than the answers others have provided.  I've personally heard of contractors that got in trouble (financial) on a fixed price project and were losing money.  Then they tried to get out of the hole by asking for big up front down payments for cash flow on subsequent projects. Thankfully it's not been my personal experience, but it has been the experience of others whom I've helped.  I think this is a more common problem with smaller contractors, many may be great craftsman, but not good businessmen. 

For major projects involving contractors, I have been asked for proof of ability to pay and I have no issue with that. 

I just managed a LARGE concrete driveway replacement for my mother and the contractor wanted 50% up front.  I told him I wasn't comfortable with that and we settled on 25% to start and the remaining progress payments based on completed work.   He was OK with that and it turned out well.  Sometimes you just need to push back and negotiate.   I could write a lot more here regarding this, but need to not allow the perfect to be the enemy of the good!