Budget deficits that are projected to rise for years are straining the plumbing of the U.S. financial system, making it harder for the Federal Reserve to manage the interest rates that influence how much consumers and businesses pay to borrow.

In September, the Fed was forced to intervene in money markets to quell a brief but alarming spike in short-term interest rates. The central bank says it is prepared to handle any funding pressures that might arise before year’s end in the $2.2 trillion market for repurchase agreements,...