A critical question for Sen. Rand Paul’s effort to expand oversight of the Federal Reserve’s interest-rate decisions is whether he could win support from the central bank’s leftist critics in Congress.

But one of the Senate’s most prominent liberal Democrats says she’s not on board. Sen. Elizabeth Warren (D., Mass.), a member of the Banking Committee and an outspoken critic of the Fed’s oversight of big banks, said she does not support Mr. Paul’s proposed legislation, which she said could have “dangerous” implications for monetary policy.