WASHINGTON—As if conjuring up the spirit of his bank’s founder, Jamie Dimon is planning to take the place of the U.S. government if it goes into default—at least as far as his clients’ federal benefits go.

At a meeting of the Institute of International Finance on Saturday, Mr. Dimon, the chief executive of J.P. Morgan Chase & Co., said he expects a deal to be reached between the White House and Congress that will raise the debt ceiling before the borrowing capacity is otherwise forecast to be exhausted on Oct. 17. But in the event that the government runs out of cash to make a $12 billion Social Security payment due on Oct. 23, J.P. Morgan has a plan.

Mr. Dimon said his bank would fund the $6 billion to $8 billion in government benefits that the bank processes each week for its clients, even if the government doesn’t actually pay those obligations.