The down payments demanded by banks to buy homes have ballooned since the housing bust, forcing many people to rethink what they can afford and potentially shrinking the pool of eligible buyers.

Last week, the Obama administration called for gradually raising down payments to a minimum of 10% on conventional loans, meaning those that can be bought or guaranteed by mortgage giants Fannie Mae and Freddie Mac. And mortgage data show that private lenders are already pushing sharply higher the required down payments, mainly to...