In our area 10% is excessive. Speaking as a listing agent who works in your area (Skokie is just down the street) ... what we're looking for is enough money 'on tap', to keep you from just changing your mind and walking away.
If you're asking me... $1,000 on a $250,000 home is not enough. (I know, I know... in some areas, some regions that's typical... but not here in Skokie)... I'd be looking for a minimum of $5,000, and preferably $10,000. But, since they've already accepted your contract with only $1,000 on it... they can't just change it unilaterally.
Talk to your Realtor for more information.