Hold the house off the market for applicants?

[Bienes Raices]

Some people came to see the house today. They seemed pretty nice to me on a personal level. However, they said they couldn't come up with the rent and deposit until March 1. At least part of their income comes from Disability or some similar program, and they get that money on the first of each month. The move in date would be around March 5.

I agreed to this verbally without thinking, and now I'm uneasy about it. What if I hold the house off the market for the next couple weeks and then they don't move in for some reason? What would you do in this situation? Try to get $100 deposit to hold the house for them until March 1?

I gave them the applications to take home and fill out. They are supposed to get the apps back to me tomorrow with the app fees.
So they haven't paid anything yet.

Thanks!