Controlling a 59-seat majority in the 100-seat upper house of parliament, senators from Prime Minister Donald Tusk's governing Civic Platform (PO) liberals justified their refusal saying Kaczynski wanted to use the referendum to spark fear among voters about the future of Poland's public health service.
Legislation proposed by the liberals and adopted by the lower house of parliament this week to reform the ailing sector foresees the commercialisation of public health facilities by transforming them into companies under commercial law, whose capital is held by local authorities.
Kaczynski and the opposition conservative Law and Justice (PiS) party of his identical twin brother Jaroslaw oppose the move, slamming it as the first step towards privatising the health service.
The president has said he will veto the PO-backed legislation unless it is approved by Poles in a referendum.
Under the Polish constitution the president is able to call a referendum, but must first seek the Senate's approval.
Burdened by huge debt and chronic underfunding, Poland's health service suffers from long waiting lists, causing many patients to seek treatment in the burgeoning private sector.