We get 1/3 down the day we sign the contract and other paperwork. If you have some of their money they are more than likely to stop shopping. If they ask you the famous question:
"when could we get started?"
And, you are 2-months out, you better do two things. First, explain why your company is worth the wait. Next, get a deposit. Because, if they can find someone else to do it sooner and they have no monies invested with you, then you just lost your client.