The President-backed effort to set broader rules for US crypto markets is nearing a political deadline in Congress as banks press lawmakers and regulators to block stablecoin companies from offering rewards that resemble interest on deposits.

The fight has become one of the central unresolved questions in Washington’s crypto agenda. At stake is whether dollar-linked digital tokens remain focused on payments and settlement or gain features that make them more competitive with bank accounts and money market funds.

The Senate’s market-structure bill, known as the CLARITY Act, has stalled after negotiations broke down over so-called stablecoin yield.

Industry participants and lobbyists say late April or early May is shaping up as the…