For many households trying to improve their finances, tossing out pitches from the bank has become almost automatic. But in recent weeks, Chase has been fanning special letters out to consumers with an offer that it urges them not to refuse.

“Your debit card may not work the same way anymore, even if you just made a deposit. Unless we hear from you,” the message, emblazoned in large red type, warns. “If you don’t contact us, your everyday debit card transactions that overdraw your account will not be authorized after August 15, 2010 — even in an emergency,” with “even in an emergency” underlined for emphasis.

As the government cracks down on the way banks charge fees for overspending on debit cards, the industry is mounting an aggressive campaign aimed at keeping billions of dollars in penalty income flowing into its coffers. Chase and other banks are preparing a full-court marketing blitz, which is likely to include filling mailboxes with various aggressive and persuasive letters, calling account holders directly, and sending a steady stream of e-mail to urge consumers to keep their overdraft service turned on.

Starting this summer, banks must get consumers to agree, or “opt in,” to a service covering purchases on a debit card when there is not enough money in their account. The Federal Reserve has ordered the same restriction for banks that want to let people withdraw more than their balance at an automated teller machine. Many banks now automatically provide such coverage for fees of up to $35 or more.