Under Gillibrand’s proposal, Americans could cash paychecks and deposit money in accounts free of charge at each post office location. Deposits would be capped at the larger of two amounts ― $20,000, or the median balance in all American bank accounts.

The postal banks would be able to distribute loans to borrowers of up to $1,000 at an interest rate slightly higher than the yield on one-month Treasury bonds, currently about 2 percent.

A postal banking system would be an alternative to the for-profit payday lending system, in which people routinely pay triple-digit fees to borrow money for bills that come due before their next paycheck. The average payday loan of $375 typically costs a borrower an additional $520 in interest and fees, according to Pew Charitable Trusts.

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More than one-quarter of Americans households (34 million homes) are either “unbanked” ― meaning they lack someone with a bank account altogether ― or “underbanked” ― relying on payday loans or other so-called alternative lenders to supplement the services of a traditional bank.

Their predicament shows how expensive it is to be poor in America. The average underbanked household has an annual income of $25,500, and spends nearly 10 percent on alternative financial products and associated fees, according to a 2011 KPMG study.